I have my year-end exam in 2 days and i've been trying to understand this thing for the last 2 months(i am very weak at calculus)! i am so happy that i reached this place and was able to learn this thing in just 12 minutes! thank you so much,you've just increased my hopes of saving the semester! :)
Nobody, I mean nobody explains calculus better than you do. Ignore those thumb down those are people who can't explain closer to what you do. We appreciate you. Thanks
You did a great job explaining double integrals to polar coordinates in this video. I went from having very little knowledge in this subject to being able to solve problems. Thanks so much!
Thanks for this. My book has iterated integrals in polar, cylindrical and spherical coordinates all packed into one chapter and so the author just glances over all three. So yea, thanks again, and thanks for being so thorough. You saved me a lot of headache and frustration.
Excellent video. 5 *'s. You really helped me understand integration where you've to convert co-ordinates from Cartesian -> Polar. Thank you so much. The folks crying about the limits being 4 rather than 2, cause u=r^2 may be correct, but they're just being pedantic imo. You still got the right answer!
Great video!! One thing I noticed though: when you u-substitute for r^2, you didn't find new bounds of integration in terms of u and therefore wrote a false statement by leaving the bounds in terms of r. You rectified your mistake in the next line but my calculus professor will mark points off for that on an exam and I am hyper-vigilant of that mistake. He said to, in the least, leave it as an indefinite integral until you back-substitute for u.
Yes. The dud(theta) upper integral limits(just above the centre of the screen view) of the right integral sign should be 4. Krista corrects it on the next line when she goes back to using 'r' and using 2 for the upper integral. Now hopefully this will help solving an integral equation using the angle 'theta' to get a 2d solution of a second order random field. We will see....
last semester i missed a lot of calculus classes but with the help of your vids together with other guys vids on youtube i passed my calculus exam as though it was some kind of test on general knowledge.Now look at me, i am missing classes again this semester :p
If using the u substitution don't we have to change our interval? So in our case we would have to put our intervals (0,2) into u and we would get a new interval (0,4) with which we continue to calculate.
7 years ago when i was in 6th grade, this video was uploaded i had no clue what calculus meant. fast forward 7 years , still i have no clue and thats why iam here . thanks for uploading this video.
Now I am feeling confident to evaluate all this type of integrals. @9:32 Limits should be changed for 'u'. Great explanation! And btw, you have lovely voice 😊
Great video thanks. One question though: because you did u-substitution, do you not have to change your upper/lower bounds for du? In this example, u=2r so therefore the bounds should be u=2(0) = 0 for lower and u=2(2)=4 for higher? Or is it a rule that when you sub back in r^2 for u, the bounds should remain the same? (I hope I am making some kind of sense).
You're making perfect sense, I know exactly what you're talking about. Technically, you should change the limits of integration when you make a substitution. However, you only need to change them if you plan to evaluate over the interval WITHOUT back-substituting. If you back-substitute, then you'd just have to change the limits of integration back to what they were originally. Since I always back-substitute, I don't worry about changing them. I hope that helps clarify!! :D
For simplicity I would integrate the theta first and leave it outside as a constant, since you are always going to get a constant for theta with these types of problems. It eliminates some of the mess of the integral and you will arrive at the same exact answer without extra Algebra.
you only have to change limits of integration if you don't back-substitute. since i eventually changed my u's back to r's, i can still use the limits of integration with respect to r. :)
This was an example we did in class, and it was very rushed and done in half the time. You go at a perfect pace and I understand it so much better now. Can you be my professor?
Great video! I have only one objection - when you explain, you can´t skip even a simple steps. You did not explain why the substitution for x and y is x=cos() and y=sin() - that is really easy to figure out, but that´s because you understand it - but someone who watch this is watching it because he does not understand it - or maybe he does but needs to review and this would be really helpful to show as well. Also you did not explain why we need to add r to the integral when substituting the dy dy for dr - and that would be really helpful too :) Keep doing a great work, you help a tons of people and take this just as an advise to make it even better :)
If a professor went back and reviewed material from prereq classes every time that material was used again, then a typical 50 minute class would take 2 or 3 hours. Sorry to be blunt, but anyone learning this topic should already know that cos(theta)=x/r and sin(theta)=y/r. But of course it would be ok to ask the professor or a TA that kind of question in office hours, since that would not delay the class.
Great video! I was absent in class due to sickness when this was taught and so I had a difficult time catching up. But this really helped a lot. Thank you! You just gained one more subscriber :D
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I like how you don't skip any steps. I learn really well because of that! THANKS AGAIN!
Can you please specify why dx.dy gets replaced by rdrd(theta) ?
@@AGNIVO-kf2bl dude, it's easy, not even worth mentioning, just do as they say and don't think too much))
I have my year-end exam in 2 days and i've been trying to understand this thing for the last 2 months(i am very weak at calculus)! i am so happy that i reached this place and was able to learn this thing in just 12 minutes! thank you so much,you've just increased my hopes of saving the semester! :)
vatsalya singh I'm so glad to hear that! Good luck on your exam, I hope it goes great!
:)
How did it go , buddy ?
@@niket9394 haha it went okay enough for me to graduate out of college lol
@@My_NameJeff I am glad. Hope you're doing great in your life now 🙌
thanks, this helped. My Calc 2 prof last year skipped polar coordinates altogether so now I'm figuring this out on my own
Your explanation is clear, thorough and succinct. I've never seen that before for math videos. Please post more videos.
Great video, very clear instructions!
I like that every single step gets explained, even those well known little ones, so you can't overlook anything.
Nobody, I mean nobody explains calculus better than you do. Ignore those thumb down those are people who can't explain closer to what you do. We appreciate you. Thanks
I understood each and every concept behind the question. Thank you ma'am to explain with such a great method of teaching. 😀😀😀
How am i just discovering this channel???????????? You're the BEST. Thanks!!!
Can't live without Krista during coronavirus thank u so much
You're welcome, Chen! Hope you and your family are safe and healthy! :)
I don't know what to say. I'm just really glad that I stumbled upon your video. Thank you so much for this clear and simple explanation. 😭❤
You’re the best calc explainer yet
That’s literally one of the problems I have on my homework. 😂
Wow you have solved it and nailed bro😎😎
yooooo same 3 years later
@@mariorafaelbritopavon456 yooooo same 4 weeks later xD
@@bilalrahim2076 same lol It's in the stewarts manual which is used worldwide sooo.... Makes sense !
X2
this video makes me want to burn my calculus book
You did a great job explaining double integrals to polar coordinates in this video. I went from having very little knowledge in this subject to being able to solve problems.
Thanks so much!
+Carl Ellis So glad I could help!
Krista is the Queen of Math!
Thanks for this. My book has iterated integrals in polar, cylindrical and spherical coordinates all packed into one chapter and so the author just glances over all three. So yea, thanks again, and thanks for being so thorough. You saved me a lot of headache and frustration.
+Rachel Nanshija Thanks for the comment. Glad I could help!
OH MY GAW... KRISTA... THANK YOU. I WAS STUCK ON THIS FOR SO LONG BEFORE I STUMBLED UPON YOUR VIDEO!!!
:D
I know this is years after you made this video, but thank you so much! You are a life-saver!!!
You're welcome, Spark, I'm so glad I was able to help! :D
Excellent video. 5 *'s. You really helped me understand integration where you've to convert co-ordinates from Cartesian -> Polar. Thank you so much. The folks crying about the limits being 4 rather than 2, cause u=r^2 may be correct, but they're just being pedantic imo. You still got the right answer!
best teacher who saved my semester :)
legit tho
Good maths steps am really behind on how to find the boundary region and on how to get the limits of a double integration needs your help
Your explanations are really clear and your though process/method is beautiful... Thank you…
Mthabisi Bokete You're welcome, I'm glad you like the videos!
This is the best explanation. You explain the concept clearly. Thank you so much
Your tutorial is still live here, thanks for the wonderful explanation you got my finger
Great video!! One thing I noticed though: when you u-substitute for r^2, you didn't find new bounds of integration in terms of u and therefore wrote a false statement by leaving the bounds in terms of r. You rectified your mistake in the next line but my calculus professor will mark points off for that on an exam and I am hyper-vigilant of that mistake. He said to, in the least, leave it as an indefinite integral until you back-substitute for u.
I noticed that too.
Derrek Schmitz , you are right after substitution, we have to make changes in limits according to the substitution.
Yes. The dud(theta) upper integral limits(just above the centre of the screen view) of the right integral sign should be 4. Krista corrects it on the next line when she goes back to using 'r' and using 2 for the upper integral.
Now hopefully this will help solving an integral equation using the angle 'theta' to get a 2d solution of a second order random field. We will see....
I've always re-subbed the U value back in and then evaluated for the variable in this case r. it works both ways.
Yea..
You are literally my favorite. All your videos are really clear and I actually learn :)
Been watching your vids for a year now, they are always so clear, thanks so much dear :)
inteusproductions You're welcome, glad they've been helping!
You explain things much more succinctly than any of my past teachers/lecturers :)
Thank you very much!
I can only concluded that you're better than my further calculus lecturer!! Thanks for your detailed explanation!!
you're welcome, i'm so glad it helped!!
I seriously appreciate all of your videos. Thank you. :)
You're welcome!
Pete Dietl me too
Thanks! I'm a big fan of your teaching style.
Just a few hours before my exam, you are a life saver🙏
I hope the exam went great! :D
The best explanation I’ve seen so far. Superb! Wish you were my lecturer
I'm so glad you liked the video! :D
Ohhhh, the good ole multi calc days. Probably the best calculus there is!!!
i have learned a lot from you. thank you so much for sharing this lecture!
i always get stuck while solving this problem, but i had almost mastered it. Once again THANK YOU very much.
last semester i missed a lot of calculus classes but with the help of your vids together with other guys vids on youtube i passed my calculus exam as though it was some kind of test on general knowledge.Now look at me, i am missing classes again this semester :p
LOL, well I'm so glad the videos helped!!
so so so happy i found this!!! LIFE SAVING
+Cesar Solorzano I'm so glad it could help!
just great. i watched a lot of video on this topic but this one just made my whole concept clear. thank u so much.
If using the u substitution don't we have to change our interval? So in our case we would have to put our intervals (0,2) into u and we would get a new interval (0,4) with which we continue to calculate.
I caught that too I believe you are correct
never mind just finished the video she substituted back for r
She’s the best teacher ever
yes, this is usually calc 3 stuff. :)
You are really amazing. Thanks for providing free lectures.
My pleasure, Dawlad! I'm happy I'm able to help! :D
7 years ago when i was in 6th grade, this video was uploaded i had no clue what calculus meant.
fast forward 7 years , still i have no clue and thats why iam here . thanks for uploading this video.
Lol, you bet! I just hope the video helped! :D
probably the best video out there of explaining this example!!!
Thanks! :)
seriously you're like khanacademy 2.0, thank you for the videos you're a life saver.
I'm glad they're helping! :)
SERIOUSLY. You have been leading me to the promise land this semester, thank you so much.
Now I am feeling confident to evaluate all this type of integrals. @9:32 Limits should be changed for 'u'. Great explanation! And btw, you have lovely voice 😊
Great video ! Thanx for taking the time out for this. :)
This is so much better than the way my teacher explained it, or at least tried to.... Thanks!
You're welcome, glad it helped!
Thanks. I've been trying to understand Maxwell's equations and the vids on double integrals has been helpful
i love you really .. math without you like coffee without sugar .. :) thanks and keep going
Thank you very much for this beautiful explanation! It's helped me a ton in understanding double integrals!!! 😍
Glad it was helpful, Ishaan!
Oh thank you! You saved my time and life. I am grateful to you
What a coincidence! I was stuck at this problem when I decided to check your video for help.
Excellent explanation! Really thankful for the clear example.
Thanks! I'm glad it could help!
Thank you mam it is very easy to learn from your videos rather than from class
You're welcome!
Great video thanks. One question though: because you did u-substitution, do you not have to change your upper/lower bounds for du? In this example, u=2r so therefore the bounds should be u=2(0) = 0 for lower and u=2(2)=4 for higher? Or is it a rule that when you sub back in r^2 for u, the bounds should remain the same? (I hope I am making some kind of sense).
You're making perfect sense, I know exactly what you're talking about. Technically, you should change the limits of integration when you make a substitution. However, you only need to change them if you plan to evaluate over the interval WITHOUT back-substituting. If you back-substitute, then you'd just have to change the limits of integration back to what they were originally. Since I always back-substitute, I don't worry about changing them. I hope that helps clarify!! :D
For simplicity I would integrate the theta first and leave it outside as a constant, since you are always going to get a constant for theta with these types of problems. It eliminates some of the mess of the integral and you will arrive at the same exact answer without extra Algebra.
Thank you big sister , my doubts were regarding ,that how to take theta, which is cleared in one example , thank you for your help🙏🙏
I am no longer lost, thank you so much!!
Glad it could help!
Great timing! :)
Thanks a bunch Krista for such awesome an explanation. Really helps, especially in evaluating the limits, a point where I am always confused...
You're welcome, Farrukh! I'm so glad it helped! :D
You are the absolute best. You and Sal and JustMathTutoring are the best RUclips teachers. Thank you guys, you are appreciated!
Aw, thanks! That's great company you listed me with... I'm so glad I can help! :)
you only have to change limits of integration if you don't back-substitute. since i eventually changed my u's back to r's, i can still use the limits of integration with respect to r. :)
wish me luck for my exam tomorrow. my lecturer taught this for 2 weeks but i understand your 12 minutes video better. thanks
I'm so glad the video helped, and I hope the exam went great! :D
Good i have my doubts in multiple integral but after watching this video i clear my all confusion thank you and watching from nepal
I'm so glad the video helped, Sumit! :)
Glad I could help! :)
super clear. easy to understand every step. thanks.
Thank you very much, your explanations are helping me maintain an A in calc 3.
That's so awesome! Thanks for letting me know! :)
Wow read some stuff about this on some other sites and understood nothing then I watched this 13 min long video and now understand everything THANKS!
Love that! I'm so glad it could help! :D
thanks it was very helpful.actually i saw only one video and could solve the rest. ur explanations are too good .well thanks again.
For the angle in this question is from 0 to π\ 2 because it says the area is confined between the function x and y axis
This was an example we did in class, and it was very rushed and done in half the time. You go at a perfect pace and I understand it so much better now. Can you be my professor?
I'm so glad the video made sense and helped clear things up!! :D
Excellent, saved me so much time for my exam studying !
I hope you rock the exam! :D
Wow, that was immensely thorough. Thank you!
You're welcome!
Thanks! you have no idea how much trouble i had to understand this before.
You're welcome! I'm so glad it helped!
You are simply the best! Thank you!
You make it look so easy!!! Thank you so much for your videos!!!!
These videos got me through university! Thank you so much
Thank you maam...U did really saved me with the lesson. ....
Explained very well
You're welcome, mohammed! I'm happy to help! :)
Hi, isn't the o-2 bounds suppose to change to 0-4 when using the u-substitution
Wonderful explanation, thanks!
Very clear explanation. Thanks
You're welcome, I'm glad it made sense! :)
Nice and clear explanation!
Thanks!
Great video! I have only one objection - when you explain, you can´t skip even a simple steps. You did not explain why the substitution for x and y is x=cos() and y=sin() - that is really easy to figure out, but that´s because you understand it - but someone who watch this is watching it because he does not understand it - or maybe he does but needs to review and this would be really helpful to show as well. Also you did not explain why we need to add r to the integral when substituting the dy dy for dr - and that would be really helpful too :)
Keep doing a great work, you help a tons of people and take this just as an advise to make it even better :)
Thank you, I appreciate the feedback! :D
If a professor went back and reviewed material from prereq classes every time that material was used again, then a typical 50 minute class would take 2 or 3 hours. Sorry to be blunt, but anyone learning this topic should already know that cos(theta)=x/r and sin(theta)=y/r. But of course it would be ok to ask the professor or a TA that kind of question in office hours, since that would not delay the class.
Really helpful. Double integrals were amazingly easy until we got to this point, thankfully now they're easy again.
Glad I could help! :)
You're the only reason I passed my class.
I'm honored, and I'm so glad you passed! :D
It helped me a lot.
May Allah (the one and only) reward you.
Thank you from Pakistan.
You're welcome, Abdul! I'm so glad it helped! :)
Great video! I was absent in class due to sickness when this was taught and so I had a difficult time catching up. But this really helped a lot. Thank you! You just gained one more subscriber :D
Much better than my teacher! Thanks soo so much!
Thanks so much Christa!
this video made concepts more clear..
+Apramey Poojar Great! I'm so glad it helped!
whenever we do a substitution method,we have to change limits .but u directly done
I enjoyed every moment when she said Theta ❤️❤️
Hey thanks mam for giving me a such good explanation on this topic it really helps me for understanding this topic well
Oh good! I'm so glad it helped!
Thanks Mam This is very helpful for me.My paper of Calculus 3 is on Monday(06-02-2017) and I hope I will do it very well.Again Thank You.
I'm so glad it helps, and I hope you do great on your exam tomorrow! :D
Thanks Again Mam Today I have done my paper very well
I'm so glad, great job! :)
My prof gave these problems for hw without actually going over them in class. You save my life. As if school is life.>.> Nope .......but thanks a lot.
+saad anwar So glad I could help!
this video was too helpful for me thank you for publishing this video
+Vignesh Adithyan Glad I could help!
very well explained madam..calculus with your sweet voice..its like icing on cake..;-)
+Amit Kumar Thank you very much!
Great video! Thank you so much krista!
+Praful Kamdar You're welcome, Praful!
Semester saving videos, very nice tutorials, GOOD WORK! keep helping us. And please reply to comments
Thanks! And I do my best to respond when I can. :)