Anybody who said THIS was the simpler approach(compared to the prior vids.) was clearly baiting you into flexing your mathematical mind. And for that, i thank them. I'm doing some math related academic upgrading, and your videos are the first math related ones I've begun enjoying. Thank you for that.
@syed3344 yep i agree this is some elementary integral, i follow along the video not knowing the initial solution and when i see it at the end of the video my mind went “damn its just 2 quarter of circle and a smol square”
Me being jee aspirant of 12th standard can confirm that yes we do this kind of questions a lot in chapter application of integrals😅 Btw it was not difficult but just lengthy and satisfying after getting an answer
I'm from Brazil. Although I studied calculus a bit for my college degree (Economics), I've never studied or used it again for decades. Your channel has been a fun and educational ride thru the memory lane. Keep up with your marvelous work.
Following you from Halifax Nova Scotia Canada. I'm a 73 year old geek. I find your videos extraordinary and take me back to high school and freshman year at U of W. Thank you for making them.
I’m from California, I’m currently wrapping up the Calculus course triathlon at my school after taking a semester’s worth of a break. I wanted to save some videos to get me back into this subject and your channel has been one of the best ones by far!
I'm from Porto, Portugal. I am retired and I am not and have never been a Mathematician. I really like Mathematics and, even though I sometimes don't understand everything, I think that your resolutions are magnificent. Congratulations and thanks for sharing.
I’m a licensed chemical engineer here in the Philippines. It’s been exactly 10 yrs and 3 months since my graduation in College. Love seeing integrals and makes me want to review it again. INTECAL is my favorite math subject back then hehe
I'm from Ohio, USA. My wife is a 7-12 math teacher. The Algorithm brought me to your channel and I was so excited to share your content with her. I'm >20 years out of school and never took a math course more advanced than Calc II but I absolutely love math (I should have at least minored in math, in retrospect). We both enjoy your content very much. Thank you for these posts - they're always fun to watch, especially when you take a different approach than I would and it gives me new perspectives.
I'm from Philippines and currently studying integral in this upcoming semester. I am amazed on how you answer this problem for several times and also I love all of your geometry problems.
Chile! I watch your videos till the very end. It's very satisfying to see the end result and hear your "how exciting". Your explanations are clear and straightforward, I love their minimalistic style.
I'm from Colorado. I've always loved and excelled at math, but I've let myself stagnate in the last 10 years. Your videos are reawakening the passion and interest I used to hold!
you can actually halt the calculus after finding the definite integral of the green square 0 to 5. because you can see that the red shaded region is symmetrical along the (10,0) , (0,10) diagonal. so simply add the area of the 5 by 5 right triangle to the green circle's integral you calculated... and then double the result to complete the symmetry of the red-shaded region.
I’m from India , and I am studying for IIT , whenever I am bored (from chemistry ) I just come to see your videos and freshen up. These videos are actually really fun to watch them them step by step and the level of questions is quite good (challenging) and you just make them so easy .
How are the papers these days? Tough? Easy? Back when we were preparing, our standard set was 1996-2004 papers. What's considered the "standard" set these days?
Just spotted this tonight. It’s 1 a.m., and I found this so challenged my memories of Calculus. You know I’m in Boston, and I do think the “other” method was MUCH easier. H. E. Always a pleasure to see/hear you.
after you found the area under the green circle .. you can multiply it by 2 to get the similar section under the second (blue circle) and then add the red square (where X is placed on the graph) its area should be 5x5 .. a faster shortcut to same answer 🙏 well done .. love your videos❤️
I love you and your context Andy! Keep it up! I did have a question- how did you get into math, and what’s your education level/occupation? (PS, Texas)
wow, I expected calculus to be faster at finding a solution for this, good job finding the u-substitution for the first integral (from Ukraine, living in the US)
I’m from Thailand. I have been watching your videos for months and really love it. This calculus approach is fantastic and definitely easier for someone like me, who is completely comfortable with graph and integration because the geometry ways are too much for me. Keep up the great work!
Excellent one! Here from Argentina, really wanted to go through all the video although you could have "cheated" by stating that the second part was the area of the first part plus the square below... But you proved it also with the sustitution, so kudos!!! Thank you very much!!!
India! Miss the time I used to solve calculus questions like a boss during my undergrad! Had stumbled upon this page randomly and it's kinda nostalgic to see all this now after almost a decade! Bet I'm the lone few who are happy seeing calculus! Cheers.
Hello from Scotland :) Love the videos, always perplexed looking at the problem before the explanation, then in awe watching you solve it step by step :) I am not a mathematician but absolutely love the videos!
North Carolina, It has been 30 years since I touched calculus and I have forgotten a lot. I love your geometry videos and have used them a lot to help my children in school.
I'm from South Africa, currently studying my masters in Industrial Engineering. I came across your channel on TikTok, and it led me to your YT channel. U make maths problems look easy I must say
I took calculus 3 years ago in highschool and ive almost completely forgot how to do most things in it. Ive now started working towards a computer science degree in which ill have some more advanced math classes so these videos are a great way to get back in the problem solving mindset.
I'm from Ohio ... it's been, I hate to admit it, about 28 years since I took a calculus class but I really enjoyed this, brought back memories of the tough questions.
Fairview, TN. Andy, your videos are terrific. I aced algebra, trig, and geometry in HS, but I never had calc. Got to engineering school in college and both calc and dif eq crushed me. Listening to you has lecture helps me see some logic in calc the same way i saw it in my HS mathematics courses.
I'm from Asia! I found this channel a few months ago about a geometry question, and this channel has really sparked my interest in mathematics. Thanks Andy!
From Libya, i hated maths mostly cuz of teachers being unprofessional with math concepts, But kept studying and your videos bring me back passion to continue. Keep up the good work 👍🏻
Having fun watching from Lethbridge, Alberta, with my first-year university son who's taking calculus. He seemed to understand what you were talking about.
I’m from the UK, and now nearly 30 years out of college. I was a maths and engineering major, and always loved the simplicity of geometry… and hated calculus! I love the videos and frankly don’t know how you get the ideas to put together. Well done!!
I really don't know how integrals work but I liked this video. The way you solved it was really clean and if i knew the properties of integrals i would've understood it without even needing to pause the video.
enjoyed that a lot, although I don't know enough to follow 70% of it going to go watch the other videos on the same problem shortly from Texas, living in Japan
It's mind blowing. I haven't studied integrals yet but i think, i'm gonna do it on my own (because i study humanitarian sciences more than real). These videos just show how math is various. Unusual problems also take part here. Keep it up! (greetings from Moldova)
calculus is absolutely beautiful and introduces movement into math as basically it all rests on getting closer and closer to something you cant touch. start with derivatives they are basic and you dont need to know a lot of precalc to understand some basic ones. once u get to integration it'll be magic how closely they connect.
I am from Bangladesh and I recently finished by A Levels. Find out abut channel only recently, this videos stuck out to me since I was doing solving similar problems w/ calculus in my Pure Mathematics course.
I’m From Egypt, I’ve always been fascinated by math and this channel only made it much more fun, I haven’t been on the level of grand calculus yet, yet your videos make it seem more fun than how some other aspects of learning maths would go by it. Your videos are awesome dude!
I am from Bosnia studying electricsl engineering and this is just beautiful, since I am a first year student and haven't even begun doing this of this sort. But this gave me an idea how to calculate the are of a curve this is very informative thank you. Enjoyed the vide a lot ty again for good content
Stephen from NC. Thanks for this video. I’m slowly starting to understand it and I take Calculus 1 in the fall. Yours and several others videos are really helping!!!
In college, even though my degree didn't require it, I wanted to learn calculus. I wanted to be a guy who "knew calculus". I started taking math classes working in that direction, but required classes took priority and I never ended up taking any calculus classes. Later I started working through online classes, but got busy and didn't finish. I bought a calculus text book and didn't get very far in that. Well. I just watched this video and...... I think I've now officially lost interest in ever learning it. That was crazy! I can't imagine how much work I'd need to put in to learn all that. (I guess I'm still interested, but can't imagine ever having the time or energy....) I'm from San Diego, btw. I love these videos, in a strange way, the way you take these challenging problems and break them down makes it feel like maybe my life's problems also have solutions.
I'm from Brazil, and I have an extremely poor basic math background. However, I still really enjoy your videos and hope to be able to do some math myself one day.
Hello, instead of the previous solution method, you could easily divide it into a smaller square and 2 quarter circles or a half circle, which is easier to solve.
Greetings from Kuwait 🇰🇼, and I just love your videos! As an engineer I’d probably go immediately to calculus to solve the problem - even though dividing the shape into quadrants looks easier! - because I’d use Mathematica to do the grunt work!
It’s been a while since I’ve taken calc 3 so I’m pretty rusty in all of this. But if I remembered how to do it exactly there is a better approach. We can rephrase the equation to use polar coordinates of course. But we can also move the shape so this makes more sense. If you rotate the shape 90 degrees counter clockwise and center the origin at the top right intersection of the circles (where the two diameters meet), it makes polar coordinates easier. Furthermore, we can use the diagonal symmetry to realize that this integral from 0 to pi/4 will be the same as pi/4 to pi/2. So we can just evaluate half of it and multiply it by 2. So then the bounds of the integral would just be 0 - pi/4 and the whole thing would be multiplied by 2. Using these bounds, you can find the integral in polar coordinates of the square area, and subtract it by the integral of the circle shifted by 5 to the right. So it would be the subtraction of 2 rather easy polar integrals rather than all of this
I found it easier to do the following: Calculate the Area of the Square. Both semi-circles inside the square are of the same r, so calculate the Area of the circle once, to find the unmarked area. Since we are counting two semicircles that overlap, we can use the fact that they have the same radius. Using pythagoras we find the h(Line). Now we can use the properties of lens formed by 2 circles to calculate the Area of the lens. Once found: Area not marked = Area of the circle - Area of lens. Area marked = Area of the square - Area not marked. I rounded to 2.d.p. and got 35.77.
im firm Syria and i like math even though my field of work is not related to it but i really enjoy trying to solve the problem's your doing a great job 💯💯💯
Software Engineering student from Israel here, this awful war has caused the education system to come to a halt so I really enjoy watching your videos to stay sharp and remember a lot of the techniques. Praying for better times to all sides who are suffering 🙏
Anybody who said THIS was the simpler approach(compared to the prior vids.) was clearly baiting you into flexing your mathematical mind. And for that, i thank them. I'm doing some math related academic upgrading, and your videos are the first math related ones I've begun enjoying. Thank you for that.
Nah,it was definitely simpler,u don't have to use ur brain much for this method,although the method is lengthy but those r very elementary integrals.
@syed3344 yep i agree this is some elementary integral, i follow along the video not knowing the initial solution and when i see it at the end of the video my mind went “damn its just 2 quarter of circle and a smol square”
If you enjoy him, try blackpenredpen and 3b1b
The simplest solution is the one you know
Me being jee aspirant of 12th standard can confirm that yes we do this kind of questions a lot in chapter application of integrals😅
Btw it was not difficult but just lengthy and satisfying after getting an answer
I'm a math teacher in NYC and have shared a number of your vids with students on Google Classroom. Thanks!
Why do I find maths so sexy when this guy talks through a solution?
You are "sapio-sexual" 😂
(I didn't think of that, someone else said it and it stuck with me. Wish I could claim it!)
I'm from Brazil. Although I studied calculus a bit for my college degree (Economics), I've never studied or used it again for decades.
Your channel has been a fun and educational ride thru the memory lane. Keep up with your marvelous work.
Bacana, faço engenharia e me divirto vendo os vídeos dele também. Tmj
Outros do brazil!!!!!!!!
Following you from Halifax Nova Scotia Canada. I'm a 73 year old geek. I find your videos extraordinary and take me back to high school and freshman year at U of W. Thank you for making them.
I’m from California, I’m currently wrapping up the Calculus course triathlon at my school after taking a semester’s worth of a break. I wanted to save some videos to get me back into this subject and your channel has been one of the best ones by far!
I'm from Argentina. I feel like you are the best math teacher i've ever encountered
So true! Also, cheers fellow Argentinian!
I'm from Porto, Portugal. I am retired and I am not and have never been a Mathematician. I really like Mathematics and, even though I sometimes don't understand everything, I think that your resolutions are magnificent. Congratulations and thanks for sharing.
I’m a licensed chemical engineer here in the Philippines. It’s been exactly 10 yrs and 3 months since my graduation in College. Love seeing integrals and makes me want to review it again. INTECAL is my favorite math subject back then hehe
I'm from Ohio, USA. My wife is a 7-12 math teacher. The Algorithm brought me to your channel and I was so excited to share your content with her. I'm >20 years out of school and never took a math course more advanced than Calc II but I absolutely love math (I should have at least minored in math, in retrospect). We both enjoy your content very much. Thank you for these posts - they're always fun to watch, especially when you take a different approach than I would and it gives me new perspectives.
I’m a retired Mechanical Engineer from the Dallas, Texas area. Nice job with the tricky calculus.
I'm from Philippines and currently studying integral in this upcoming semester. I am amazed on how you answer this problem for several times and also I love all of your geometry problems.
Chile! I watch your videos till the very end. It's very satisfying to see the end result and hear your "how exciting". Your explanations are clear and straightforward, I love their minimalistic style.
I'm from Colorado. I've always loved and excelled at math, but I've let myself stagnate in the last 10 years. Your videos are reawakening the passion and interest I used to hold!
you can actually halt the calculus after finding the definite integral of the green square 0 to 5. because you can see that the red shaded region is symmetrical along the (10,0) , (0,10) diagonal. so simply add the area of the 5 by 5 right triangle to the green circle's integral you calculated... and then double the result to complete the symmetry of the red-shaded region.
I’m from India , and I am studying for IIT , whenever I am bored (from chemistry ) I just come to see your videos and freshen up. These videos are actually really fun to watch them them step by step and the level of questions is quite good (challenging) and you just make them so easy .
Bro if you are preparing for IIT these questions should look like baby questions
How are the papers these days? Tough? Easy? Back when we were preparing, our standard set was 1996-2004 papers. What's considered the "standard" set these days?
Just spotted this tonight. It’s 1 a.m., and I found this so challenged my memories of Calculus. You know I’m in Boston, and I do think the “other” method was MUCH easier. H. E. Always a pleasure to see/hear you.
I'm from Brazil, and I stumbled upon your channel by accident during my studies, and I'm just loving your explanations! Thanks a lot, man!
+sub +like
Pelo visto há vários brasileiros que acompanham este canal. O bom é que aprendemos Inglês e Matemática ao mesmo tempo.
@@frankstrawnation exatamente!
Mais um aqui, sugerido pelo algorítmo. Longe de saber matemática neste nível, mas vejo muita beleza!
@@frankstrawnation exato! E não é difícil de acompanhar!
after you found the area under the green circle .. you can multiply it by 2 to get the similar section under the second (blue circle) and then add the red square (where X is placed on the graph) its area should be 5x5 .. a faster shortcut to same answer 🙏 well done .. love your videos❤️
He's declared at the start that he'll use only calculus and no geometry for this one and he did just that.
I’m from Malaysia, I enjoy watching your videos. Love how you solve problems in different methods.
I love you and your context Andy! Keep it up! I did have a question- how did you get into math, and what’s your education level/occupation?
(PS, Texas)
Excellent question.
Bump
wow, I expected calculus to be faster at finding a solution for this, good job finding the u-substitution for the first integral (from Ukraine, living in the US)
Integrals can be so beautiful once you master it. Such a gorgeous solution!
I’m from Thailand. I have been watching your videos for months and really love it. This calculus approach is fantastic and definitely easier for someone like me, who is completely comfortable with graph and integration because the geometry ways are too much for me. Keep up the great work!
Sweden here. Retired dentist. Age 67. The level of math in your channel is right up my alley. Keep up the good work❤️
I’m from Rhode Island and got an engineering degree from upstate New York. The u and v substitutions made be have flashbacks to freshman year.
Bogota, Colombia. Thank you for your channel. I’m a musician, and I love the way you explain step by step every solution. ❤
Excellent one! Here from Argentina, really wanted to go through all the video although you could have "cheated" by stating that the second part was the area of the first part plus the square below... But you proved it also with the sustitution, so kudos!!! Thank you very much!!!
India! Miss the time I used to solve calculus questions like a boss during my undergrad! Had stumbled upon this page randomly and it's kinda nostalgic to see all this now after almost a decade! Bet I'm the lone few who are happy seeing calculus! Cheers.
Hello from Scotland :) Love the videos, always perplexed looking at the problem before the explanation, then in awe watching you solve it step by step :) I am not a mathematician but absolutely love the videos!
Absolutely love your videos! No fancy introduction crap.. Straight to the math.
Greetings from Kingston Ontario Canada.
North Carolina, It has been 30 years since I touched calculus and I have forgotten a lot. I love your geometry videos and have used them a lot to help my children in school.
From the UK, relearning calculus from when I first studied it 37 years ago. Loving it.
I'm from South Africa, currently studying my masters in Industrial Engineering. I came across your channel on TikTok, and it led me to your YT channel. U make maths problems look easy I must say
I'm from Carmel, Indiana. My head exploded when you said that "we've seriously cleaned up this integral". I'm just along for the ride at this point.
I took calculus 3 years ago in highschool and ive almost completely forgot how to do most things in it. Ive now started working towards a computer science degree in which ill have some more advanced math classes so these videos are a great way to get back in the problem solving mindset.
From India, watched it till the end. Loved it. I watch these for fun and it's amazing. How exciting
I'm from São Paulo, Brazil. Love your content!
Bro, this is such an underrated Maths channel. You have by far the best explanations, thank you. 😊
I'm from Ohio ... it's been, I hate to admit it, about 28 years since I took a calculus class but I really enjoyed this, brought back memories of the tough questions.
Fairview, TN.
Andy, your videos are terrific. I aced algebra, trig, and geometry in HS, but I never had calc. Got to engineering school in college and both calc and dif eq crushed me. Listening to you has lecture helps me see some logic in calc the same way i saw it in my HS mathematics courses.
Watching from Brazil here! Mechanical engineering student, so cool to watch your videos… How exciting! 👊🙌
I'm from Asia! I found this channel a few months ago about a geometry question, and this channel has really sparked my interest in mathematics. Thanks Andy!
I am from Russia and I want to thank you very much for the basics of integration. Now I am in the 10th grade and I am interested in math analysis.
From Libya, i hated maths mostly cuz of teachers being unprofessional with math concepts,
But kept studying and your videos bring me back passion to continue.
Keep up the good work 👍🏻
Having fun watching from Lethbridge, Alberta, with my first-year university son who's taking calculus. He seemed to understand what you were talking about.
Hungary, Budapest. As an engineer, i use autocad and I become lazy in geometry, but with your videos i can keep my math fresh. :) Thanks!
I’m from the UK, and now nearly 30 years out of college. I was a maths and engineering major, and always loved the simplicity of geometry… and hated calculus!
I love the videos and frankly don’t know how you get the ideas to put together. Well done!!
Seeing this video I can understand your hate.
I really don't know how integrals work but I liked this video. The way you solved it was really clean and if i knew the properties of integrals i would've understood it without even needing to pause the video.
enjoyed that a lot, although I don't know enough to follow 70% of it
going to go watch the other videos on the same problem shortly
from Texas, living in Japan
I'm from Taiwan. It's been over a decade since the last time I took a math class, and your videos make me realize that I actually quite like math.
I am from Romania but I live in germany. Your videos really make my day better! Keep up the good work.
From India . u solve with smooth flow so good to watch
It's mind blowing. I haven't studied integrals yet but i think, i'm gonna do it on my own (because i study humanitarian sciences more than real). These videos just show how math is various. Unusual problems also take part here. Keep it up! (greetings from Moldova)
calculus is absolutely beautiful and introduces movement into math as basically it all rests on getting closer and closer to something you cant touch. start with derivatives they are basic and you dont need to know a lot of precalc to understand some basic ones. once u get to integration it'll be magic how closely they connect.
Hello from Denmark, and Thanks for taking up the challenge and solving the problem with Calculus
I'm from northern California and math is a hobby of mine. I enjoy your videos. Very well done. Please, continue.
I am from Bangladesh and I recently finished by A Levels. Find out abut channel only recently, this videos stuck out to me since I was doing solving similar problems w/ calculus in my Pure Mathematics course.
From England. Your videos bring back many happy memories of school maths...with an s over here.
Kilmarnock, VA, originally from Williamsburg, VA. Haven’t had calculus in over 20 years so this made my head spin. But it was a wild ride!
I’m From Egypt, I’ve always been fascinated by math and this channel only made it much more fun, I haven’t been on the level of grand calculus yet, yet your videos make it seem more fun than how some other aspects of learning maths would go by it. Your videos are awesome dude!
Chicago. Nicely done. Always enjoy your algebraic geometric and calculus calisthenics.
From Bali, Indonesia. Really cool videos on math! Thanks Andy
Great content for great memories when I had to do all that Calculus while studying Engineering (cheers from Portland OR!)
I am from Turkiye. I really enjoy with your math problems and solving methods. Keep going man🧐
I love your channel, makes me remember my days in college. Wish I was that good for geometry and calculus. Cheers from Mexico
Quito, EC. watching you solve these math problems it's mesmerizing
I'm from Vietnam, after the university entrance exam I forgot how interesting math is, thank you for reviving it in me.
From India, and I like how you seating in an empty room where nobody to desturb you, doing all this interesting math for free, thanks❤
I am from Bosnia studying electricsl engineering and this is just beautiful, since I am a first year student and haven't even begun doing this of this sort. But this gave me an idea how to calculate the are of a curve this is very informative thank you. Enjoyed the vide a lot ty again for good content
From Sweden. Thanks for the cozy headache Andy!
Im from Dominican Republic, watching your videos made me realize I need to refine my math.
Hello, from Pensacola Florida. We’re a whole family of math nerds. And we love your content.
Stephen from NC. Thanks for this video. I’m slowly starting to understand it and I take Calculus 1 in the fall. Yours and several others videos are really helping!!!
I'm from Colombia, and I'm glad that I found your channel
SW Michigan, across the lake from Chicago. How exciting.
I‘m from Germany and really enjoy your videos. Plus they actually helped me in the last exam, so thank you for that.👍🏼
I'm from Nigeria, and I just decided to watch this at 3:00AM in the morning while eating cornflakes. Best investment of my time.
Congrats on 100k subscribers
México. Thanks to your videos I'm studying my old algebra and calculous books again, this time for fun! Thanks you so much!
From Canada, nice video, just starting calculus and realizing that there is still a lot of things I have to learn still :)
Watching from Switzerland. Loved the solution with calculus!
Watching from NY! Finishing up college as a film student. Haven’t taken math since high school but it’s good to review!
In college, even though my degree didn't require it, I wanted to learn calculus. I wanted to be a guy who "knew calculus". I started taking math classes working in that direction, but required classes took priority and I never ended up taking any calculus classes. Later I started working through online classes, but got busy and didn't finish. I bought a calculus text book and didn't get very far in that. Well. I just watched this video and...... I think I've now officially lost interest in ever learning it. That was crazy! I can't imagine how much work I'd need to put in to learn all that. (I guess I'm still interested, but can't imagine ever having the time or energy....) I'm from San Diego, btw. I love these videos, in a strange way, the way you take these challenging problems and break them down makes it feel like maybe my life's problems also have solutions.
Hey, don't give up, buddy ❤️ You may have the time and energy later 😊
I'm from Brazil, and I have an extremely poor basic math background. However, I still really enjoy your videos and hope to be able to do some math myself one day.
Near Hartford, CT. I love your videos-thank you for sharing your love of math!
Hello, instead of the previous solution method, you could easily divide it into a smaller square and 2 quarter circles or a half circle, which is easier to solve.
I am from Bangladesh. I really love your videos, they're short and really informative ❤
Greetings from Kuwait 🇰🇼, and I just love your videos! As an engineer I’d probably go immediately to calculus to solve the problem - even though dividing the shape into quadrants looks easier! - because I’d use Mathematica to do the grunt work!
From New Zealand, wow that was the hard way of doing it - I'm sticking with the geometric solutions :-)
It’s been a while since I’ve taken calc 3 so I’m pretty rusty in all of this. But if I remembered how to do it exactly there is a better approach.
We can rephrase the equation to use polar coordinates of course. But we can also move the shape so this makes more sense. If you rotate the shape 90 degrees counter clockwise and center the origin at the top right intersection of the circles (where the two diameters meet), it makes polar coordinates easier.
Furthermore, we can use the diagonal symmetry to realize that this integral from 0 to pi/4 will be the same as pi/4 to pi/2. So we can just evaluate half of it and multiply it by 2.
So then the bounds of the integral would just be 0 - pi/4 and the whole thing would be multiplied by 2.
Using these bounds, you can find the integral in polar coordinates of the square area, and subtract it by the integral of the circle shifted by 5 to the right.
So it would be the subtraction of 2 rather easy polar integrals rather than all of this
I'm from Coquimbo, Chile. Amazing videos, keep going
el mejor pais de chile
I'm from India. Nice video, Andy! Been watching your videos since last week. You got a new subscriber.
I found it easier to do the following:
Calculate the Area of the Square.
Both semi-circles inside the square are of the same r, so calculate the Area of the circle once, to find the unmarked area.
Since we are counting two semicircles that overlap, we can use the fact that they have the same radius.
Using pythagoras we find the h(Line).
Now we can use the properties of lens formed by 2 circles to calculate the Area of the lens. Once found:
Area not marked = Area of the circle - Area of lens.
Area marked = Area of the square - Area not marked. I rounded to 2.d.p. and got 35.77.
Anton from Brooklyn - love your videos. Thanks!
I'm from Brazil, I really love your videos!
Man i love your approach...its so easy to follow along😊❤
im firm Syria and i like math even though my field of work is not related to it but i really enjoy trying to solve the problem's
your doing a great job 💯💯💯
Made it up to the end. Bravo from France.
From Atlanta. You're really dredging up all these Calc 2 memories of doing integrals and u substitution. Wow.
Software Engineering student from Israel here, this awful war has caused the education system to come to a halt so I really enjoy watching your videos to stay sharp and remember a lot of the techniques.
Praying for better times to all sides who are suffering 🙏