Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ruclips.net/video/lQM-0Nqs9Pg/видео.html
I have noticed this common thing in all his videos that makes it really easy to understand each problem is that he does not skip any step, skipping small basic step can confuse students, leading them to fail tests. and for saving people like me thank you so much from the bottom of my heart.
@@carmenouzon6690 Because he explains each step in detail so that you can watch and learn when you get stuck. This is what distinguishes him from the lecturers at the university.
To the organic tutor, I just wanted to say thank you so so much for all your videos, I am currently in my final year teaching, and am majoring in mathematics and science. I would not have been able to do it without your videos. Your methods are amazing and its simple to follow your explanations. God bless.
We need more people like you. Who explains. Everything. Like every step and detail. Like really in DETAIL. Even though we know some stuff. It's better for someone like you to explain in full detail. So that it is really understood. ❤
This is the first time a teacher of mine has explained a concept clearer than you. A testament to my calc II teacher a few years back, and even more so to you for being better than the hundreds of teachers I’ve had.
Self-studying for Calc BC. Oof, talk about procrastination. One of the few good things that came out of the pandemic is the shortening of the AP tests. I should probably still learn the rest of the stuff so I'm not confused later on lol.
Professor Organic Chemistry Tutor, thank you for another beautiful video/lecture on Arc Length Problems in Calculus Two. Calculating Arc Lengths in Calculus is straight forward, however, the Algebra and the Integration can get messy. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
I think it's because you've already got over the hard parts of wrapping your mind around the new information. When you come to yt...you already have a sort of foundation.. which is probably why it feels easier here.. That's just my theory cause it happens to me too
@Naomi Nagata ur right, its easy, but actually integrating some of the stuff, and especially spending 15 + minutes trying to integrate and finding out you were integrating wrongly or that the integrand is nonelementary, is just sad.
At 18:11 I'd like to also add that it helped me to just use u-substitution to let u = y^2, so you can just factor u^2+2u+1. It's easier for me to remember because we use u as the variable for u-substituting integrals as well.
@@474yx because he found the new integral by plugging the values of x into the equation that U equals and therefore found new bounds for the integral (:
Thank you thank you thank you so much for writing out all the steps. My prof goes so fast and skips stuff when writing everything and it kills me cause I just can’t catch up that quickly. Even some yt vids skip some things and I just appreciate how in depth these vids are.
The procedures to this our easy. I really wish you went more into detail about what’s happening and why we’re doing these things and explaining what the answer means and is telling us.
At the conclusion of example problem 2 around (14:00), you didn't convert the "u" substitution back to its original value (1+ x ^2/3) before making the final calculations. I'm wondering why? I'm new at this, so if it's a stupid question, you have my apologies. When I did convert it back, I got a decimal answer of 3.611. Thanks for your videos. I take extensive notes from them and follow your work closely.
@@yearofsilence when using u-substitution, you wont need to substitute it back if you replaced the a and b values with their u values before integrating. Notice he changed 8 and 1 to 5 and 2
@@geckokun2805 So if you don't change the values from 8 &1 to 5 and 2 then , in that case, you would have to substitute it back? it's been a while haha
@@yearofsilence With U sub if you find U(b) and U(a) you don't need to substitute U back in but rather directly insert U(b) and U(a) as U. I'm not sure if you can do it any other way
I found the factoring out in the 2nd problem kinda weird so I tried the approach I immediately thought of instead which was trigonometric substitution, and it actually worked as well!!
lol right aroung 25:04 I am pausing the video as I usually do, this time questioning my decisions on major, but trying to comprehend the method. Only to press play and the very next words "This is going to be a long problem" confirms that I am not overexagerating my grief.
From what i understand, if you want to keep the problem in terms of “u” like he did at 5:27 of the video, you change the limits of integration as he did. So instead of replacing u with (1 + 81x), he changed the [a,b] values to make it easier. So if you want to keep the “u”, you gotta change the limits of integration. If you plan on replacing “u” back with whatever number was subbed out ( 1+81x in this video) then you do not need to change the limit of the integration. Hope that helps for anyone who may have been confused like myself. It makes perfect sense once you understand!
because if you don't the question becomes a lot more confusing to do, factoring out the X^(-2/3) makes it easier to solve without the use of computing power.
shouldn't the index number of 2/3 be 3 and not 2 for the second one? 1/2 is a square root and 1/3 is a cubed root so I'm just confused(@10:34 in the video)
On the second problem I’m a little confused, why wouldn’t you just leave the limits of integration the same and put the equation back in terms of x after the u sub? That’s what I did and I got a different approximate answer
btw how would we know if we are to use u substitution right after finding f prime of x or first take x common outside the parentheses , create two separate square roots and then use u substitution?
He's fantastic but has a tendency to belabor simple algebraic/math operations and burn through the harder concepts -anyone else notice that? Check out Krista KIng's video (Arc Length ..) for the last problem, I think that she executes it more clearly.
i have a question about the last problem when you factor the 1/4y^-1, shouldn't the new expression have the 4y+1(y-1)^2 to account for the term that has been factored? because I see that you factor it as (4y+(y-1)^2) I feel confused in this part
At 10:34 , may anyone please tell me why did he factor out x^-2/3? Why didn't he go directly for substitution? AND THANK YOU SIR FOR ALL THESE AMAZING VIDEOSS!!
I’m also confused but I think it has something to do with the exponents being negative or something,I’m just assuming cause he did the same with the other problem
I'm not sure if you figured out as to why he changed the bounds of the integrals. If not, it's because he used the u-sub which caused him to change the bounds. You can keep the same bounds if you remember to change the u value back in terms of x.
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/lQM-0Nqs9Pg/видео.html
I have noticed this common thing in all his videos that makes it really easy to understand each problem is that he does not skip any step, skipping small basic step can confuse students, leading them to fail tests. and for saving people like me thank you so much from the bottom of my heart.
Agree
i have a c0cky teacher who skips lots of steps and then when i ask questions he says, you're supposed to kjnow because its from algebra/cal 1 etc....
01:19 f(x) = 1 + 6x^(3/2); [0, 1]
06:42 y = (3/2)x^(2/3); [1, 8]
14:14 x = (1/3)(y^2+2)^(3/2); [0, 4]
20:05 x = (1/3)(sqr(y))(y - 3); [1, 9]
Thanks bro. This vid is hard to follow if you skip around without time stamps lol
VenularSilver you got your prayer from me today my man
What’s crazy is 4 questions took him 30 minutes to explain
@@carmenouzon6690 Because he explains each step in detail so that you can watch and learn when you get stuck. This is what distinguishes him from the lecturers at the university.
To the organic tutor, I just wanted to say thank you so so much for all your videos, I am currently in my final year teaching, and am majoring in mathematics and science. I would not have been able to do it without your videos. Your methods are amazing and its simple to follow your explanations. God bless.
yes he is organic
We need more people like you. Who explains. Everything. Like every step and detail. Like really in DETAIL. Even though we know some stuff. It's better for someone like you to explain in full detail. So that it is really understood. ❤
how is getting a volume easier than getting length in calculus, HOWWWW!!!!!
Because in order to get volume you need the dimensions first.
🤣🤣
And there’s no proof for arc length of the curve however for volume formula there’s at least intuitive explanation
Someone PLEASE HELP! this is a bad question, but for the first example, he didn’t substitute u back in for what it was (1+81x) why?!?!!!!!!
@@474yx it was a definite integral
I love you so much man, you are saving me right now in calculus 2!!
@Ian Taylor How much homework do you get in college calculus?
@Ian Taylor Were the problems like part a b c defglwgwnaoeu?
@Ian Taylor Literally me right now. I'm at exactly a 60% in my calc class and tomorrow is the final, this is determining if I pass or fail
@Ian Taylor Haha thanks, you too!
@@videobyandrew homie did you pass or nah
college has been so difficult to keep up with these past few weeks that i’m reviewing all this stuff the day before the test :(
you are not the only one
lmao
i feel you
Lmao im in the one night before exams gang
@@aniketmukhia8355 got one tomorrow, can't wait to fail!
@@Elicruz2 U will not fail
This is the first time a teacher of mine has explained a concept clearer than you. A testament to my calc II teacher a few years back, and even more so to you for being better than the hundreds of teachers I’ve had.
how are you sir
Self-studying for Calc BC. Oof, talk about procrastination. One of the few good things that came out of the pandemic is the shortening of the AP tests. I should probably still learn the rest of the stuff so I'm not confused later on lol.
Professor Organic Chemistry Tutor, thank you for another beautiful video/lecture on Arc Length Problems in Calculus Two. Calculating Arc Lengths in Calculus is straight forward, however, the Algebra and the Integration can get messy. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Crazy how I can literally watch 6 min of this video and understand the topic but won’t even understand a word from my professor 120 mins lecture.
same bro same
literally
I think it's because you've already got over the hard parts of wrapping your mind around the new information. When you come to yt...you already have a sort of foundation.. which is probably why it feels easier here..
That's just my theory cause it happens to me too
@@ManoDGoat I think that makes sense, sometimes a second step by step helps a lot
Ok can I just say this: arc length integrals suck.
this is easy
Nate Mac I love calc II
King Figg The actual integration is easy. Getting into a form where it’s easily integrable is straight up annoying.
@Naomi Nagata ur right, its easy, but actually integrating some of the stuff, and especially spending 15 + minutes trying to integrate and finding out you were integrating wrongly or that the integrand is nonelementary, is just sad.
I'm now in Diff Eq and doing Laplace transform and I want to rip my hair out.
You’re videos are a lifesaver! I felt somewhat comfortable with arc length before watching, but after watching I felt confident in my work!
At 18:11 I'd like to also add that it helped me to just use u-substitution to let u = y^2, so you can just factor u^2+2u+1. It's easier for me to remember because we use u as the variable for u-substituting integrals as well.
Someone PLEASE HELP! this is a bad question, but for the first example, he didn’t substitute u back in for what it was (1+81x) why?!?!!!!!!
@@474yx because he found the new integral by plugging the values of x into the equation that U equals and therefore found new bounds for the integral (:
@@si1az0 rocket league?
@@Zoooooooooooo ?
Thank you thank you thank you so much for writing out all the steps. My prof goes so fast and skips stuff when writing everything and it kills me cause I just can’t catch up that quickly. Even some yt vids skip some things and I just appreciate how in depth these vids are.
I watched most of your calculus videos and they’re just the best thank you!!!
This mans a true genius, thank u for saving my gpa on an array of occasions
once again youve done it again. you are the best thing thats ever happened to math
I think this is the first time I find a hard example. Especially the last one.
you are the best! you've saved my butt numerous times. thank you
The procedures to this our easy. I really wish you went more into detail about what’s happening and why we’re doing these things and explaining what the answer means and is telling us.
Its probably because he goes more indepth on his patreon usually.
They need to clone Organic Chemistry Tutor and have him teach all STEM-related classes from the high school to college levels
holy shit, the last problem is actually the one that I am working on and stuck on...
I found one of my problems here, too
At the conclusion of example problem 2 around (14:00), you didn't convert the "u" substitution back to its original value (1+ x ^2/3) before making the final calculations. I'm wondering why? I'm new at this, so if it's a stupid question, you have my apologies. When I did convert it back, I got a decimal answer of 3.611. Thanks for your videos. I take extensive notes from them and follow your work closely.
I got the same thing... I think he forgot to substitute back.. :( He never answered you... sigh
@@yearofsilence when using u-substitution, you wont need to substitute it back if you replaced the a and b values with their u values before integrating. Notice he changed 8 and 1 to 5 and 2
@@geckokun2805 So if you don't change the values from 8 &1 to 5 and 2 then , in that case, you would have to substitute it back? it's been a while haha
@@yearofsilence With U sub if you find U(b) and U(a) you don't need to substitute U back in but rather directly insert U(b) and U(a) as U. I'm not sure if you can do it any other way
yo you are literally a genius. it's insane
I found the factoring out in the 2nd problem kinda weird so I tried the approach I immediately thought of instead which was trigonometric substitution, and it actually worked as well!!
Saving me in Cal 2, Thank you so much for your teaching.
you deserve my lazy teacher's salary. thank you for this.
Awesome content! The way you explain complex topics in such a simple intuitive way is just amazing! Thank you, for all the math help!
You're a patron of the arts
lol right aroung 25:04 I am pausing the video as I usually do, this time questioning my decisions on major, but trying to comprehend the method. Only to press play and the very next words "This is going to be a long problem" confirms that I am not overexagerating my grief.
Organic Chemistry Tutor, you are a legend.
I’m a bit confused on why we change [a,b] when using u sub. but thank you for this video💯
From what i understand, if you want to keep the problem in terms of “u” like he did at 5:27 of the video, you change the limits of integration as he did. So instead of replacing u with (1 + 81x), he changed the [a,b] values to make it easier. So if you want to keep the “u”, you gotta change the limits of integration. If you plan on replacing “u” back with whatever number was subbed out ( 1+81x in this video) then you do not need to change the limit of the integration. Hope that helps for anyone who may have been confused like myself. It makes perfect sense once you understand!
he basically just skipped to a upcoming step and did it there for easier understanding... you could do it later when you implement whatever u equals
@@I61void yes thank you, i’m well acquainted with these concepts now.
I am finding the arithmetic absolutely brutal for these problems
wow, is this guy the best? or what? .. THANK YOU.. you're a genius......
I deeply thank for your funny explanation and, I am awaken during the whole explanation, such brilient thanks!
you really a very good teacher..
thanks so much never been i watch a vid tutorial that is very informative n helpfull.. i loveu
You have a superb art of teaching
thank you for your calculus videos ! they are the reason i understand integrals
Thanks, using this to find the circumference of a squircle
Thank you so much for making your content free
For the second question why weren't we able to do U substitution immediately and instead have to factor out the x^(-2/3)?
because if you don't the question becomes a lot more confusing to do, factoring out the X^(-2/3) makes it easier to solve without the use of computing power.
shouldn't the index number of 2/3 be 3 and not 2 for the second one? 1/2 is a square root and 1/3 is a cubed root so I'm just confused(@10:34 in the video)
On the second problem I’m a little confused, why wouldn’t you just leave the limits of integration the same and put the equation back in terms of x after the u sub? That’s what I did and I got a different approximate answer
JG God bless you, I learned a lot from your video clips. Your instructions are very clear, to the point........
Thank you so much to this channel.^^. Really appreciate your videos. More power an Godbless.💖💖
btw how would we know if we are to use u substitution right after finding f prime of x or first take x common outside the parentheses , create two separate square roots and then use u substitution?
this man is a serious genius, NASA-stuff
that last question was gnarly
Great vid buddy! Helped a ton!
Soooo helpful.
Keep it up man😉❤
nice presentation sir JB
Thank You sir for the video, but I think starting at time 17:29, it should have been dy and not dx at the end of the integral. Am I correct?
that's what i think too
That ad of prof.David costa scared Me 😂😂😂😂😂until i came back to my sense
this man is an angel
If God asks me who should go to heaven I say you. Even tho God will never ask me that
Don't underestimate God !
Who should go to heaven? boom he just asked you
Holy crap. I once thought the same
Oh yeah boys. I’m so fucking COOKED for this exam. Great 👍🏽
this tutorial is the best
i wish i could pay you for this. thank you
u can donate to him u know
@@John-bq1lp how ??
Correction at 13:35, it is supposed to be 2/3 because you took the derivative not the integral hence multiplying gets us 4/9. Agree?
أحبببك يا أحلى أستاذ❤❤❤❤🔥🔥🔥🔥🔥
He's fantastic but has a tendency to belabor simple algebraic/math operations and burn through the harder concepts -anyone else notice that? Check out Krista KIng's video (Arc Length ..) for the last problem, I think that she executes it more clearly.
Nice channel for students 👍👌
You are doing well sir
Thanks for teaching us sir
You're legendary man
your the math goat.
Exercise .
a. f ( x ) = 1 - x ^ 1/2, with x = 0 to x = 1.
b. f ( x ) = 1 - x^ 1/3, with x = 0 to x = 1.
Hellow
Youu saved me in my first exam
Love your videos bro ❤️
2:23 WHATS 6 TIMES 3 ?
6 TIMES 3
6 THREES
this a a refrence to a meme xD
When and why do we have to change the limits of integration? I'm guessing that it has to do with u-sub but I'm unsure.
i have a question about the last problem when you factor the 1/4y^-1, shouldn't the new expression have the 4y+1(y-1)^2 to account for the term that has been factored? because I see that you factor it as (4y+(y-1)^2) I feel confused in this part
maman I really thank you and I hope you can do double integration under solid revolution topic thangs man.
7 years later still helping students out o7
Thanks. This was really helpfull
On the last question does he cancel one of the 3's twice? he cancels the 3 from 1/3 at 21.18 and then again at 22.04...
For the last one I integrated by parts and the final answer was the same. If you did it the same way as I did, it is correct as well.
At 10:34 , may anyone please tell me why did he factor out x^-2/3? Why didn't he go directly for substitution?
AND THANK YOU SIR FOR ALL THESE AMAZING VIDEOSS!!
I’m also confused but I think it has something to do with the exponents being negative or something,I’m just assuming cause he did the same with the other problem
You are great !
From india
in the first problem why do you need to change the bounds? 3:55
I'm not sure if you figured out as to why he changed the bounds of the integrals. If not, it's because he used the u-sub which caused him to change the bounds. You can keep the same bounds if you remember to change the u value back in terms of x.
Augustin Kim yeah I figured it out like 4 months ago. Thanks anyways. I passed Calc 2 with an A
@@m4rr563 congratulations, I'm taking calc 2 now.
You are the best
why don't you plug the u-sub back in? Like you immediatly put in the values without reverting U back to the x function that it stands for.
Saved my dumb ass. Thank you!!
Sir you are genius
sir, why do we find the new limit in our context above when its f(x) but not f(y)??
You only change the limit when using u-sub. If you are not going to replace u then you need to change the limit boundaries
@@asalah1672 thanks😅
Thank you. I've got one question, can anyone help. why are some limits changed using u-substitution and some don't?
the voice is really like the Lenard in Bigbang Theory.
Thank you !
Can you leave the original [_,_]? For the first you changed [0,1] to [1,82] but I left it and still got the same answer
I really appreciate you sir
there is an easy step you guys take in the last question.After derivating and taking square you add plus 1 and you can apply completing square method.
*6 minutes into the problem*
OCT: this is gonna be a long problem
Thanks!
Great video
Why do you do 1 divided (1y^-1)/4 instead of (1y^-1)/4 divided by 1 when factoring? You don't know which number is bigger. This is at 25:50 minutes in
you are like freaking Jesus
amen
I have a question? Why can’t you use usub for 9:00, wouldn’t it work out like the last problem did.
U = 1 + x ^ -2/3
Du= -3/2 x ^ -5/3
Nvm you can’t square root it after just thought about it