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! :)
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.
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....
Just a bit of advice to make this a little easier. Rather than integrating between -Pi/2 to Pi/2, you can integrate from 0 to Pi. It will make evaluating the integral much easier and will result in the same answer. If you are shifting the limits, there is the same distance between those points. If you can make 0 as your lower limit, evaluating your integral will be much easier and less of a chance to make a mistake.
You can also go from 0 to pi/2 and multiply by 2 before evaluating the integral so you get the proper area. The 2 and the -1/2 cancel out which leaves a - hanging out front. This way the only fraction you deal with is the pi/2 and like you said, using 0 as the lower bound simplifies the work load a lot.
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!
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!
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
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
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.
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
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
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. :)
Hi @krista - Is the final answer correct ? Actually, the limit of "u" was not included in the integral. You continued the integral calculations with the limits of r only. limits of u will be 0 to 4
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.
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 😊
I LOVE YOU LOVE YOU LOVE YOU LOVE YOU, U JUST SAVED MY ASS BIG TIME xDDD i have final exam tomorrow and i didn't understand anything about this subject, and was about to give up after watching every video possible, then i saw this video and thought to give it 1 last try before i drop calculus3, AND I'M SO GLAD I WATCHED IT, THANK U
+Hosam Hassan Awww thank you so much! I'm so glad that the video helped and that you decided not to drop the class. Good luck on your final, I hope it goes great!!
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!
:)
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.
Your explanation is clear, thorough and succinct. I've never seen that before for math videos. Please post more videos.
I understood each and every concept behind the question. Thank you ma'am to explain with such a great method of teaching. 😀😀😀
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
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.
thanks, this helped. My Calc 2 prof last year skipped polar coordinates altogether so now I'm figuring this out on my own
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..
OH MY GAW... KRISTA... THANK YOU. I WAS STUCK ON THIS FOR SO LONG BEFORE I STUMBLED UPON YOUR VIDEO!!!
:D
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
lovely explanation!
id look at other videos and go "wait but where did you.. but how did you.. where did that.. "
you don't get that here! :D
+greenlizardballs It makes me so happy to hear that! :D
Just a bit of advice to make this a little easier. Rather than integrating between -Pi/2 to Pi/2, you can integrate from 0 to Pi. It will make evaluating the integral much easier and will result in the same answer. If you are shifting the limits, there is the same distance between those points. If you can make 0 as your lower limit, evaluating your integral will be much easier and less of a chance to make a mistake.
You can also go from 0 to pi/2 and multiply by 2 before evaluating the integral so you get the proper area. The 2 and the -1/2 cancel out which leaves a - hanging out front. This way the only fraction you deal with is the pi/2 and like you said, using 0 as the lower bound simplifies the work load a lot.
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!
i have learned a lot from you. thank you so much for sharing this lecture!
yes, this is usually calc 3 stuff. :)
How am i just discovering this channel???????????? You're the BEST. Thanks!!!
You are literally my favorite. All your videos are really clear and I actually learn :)
I seriously appreciate all of your videos. Thank you. :)
You're welcome!
Pete Dietl me too
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!
Great timing! :)
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!
just great. i watched a lot of video on this topic but this one just made my whole concept clear. thank u so much.
i love you really .. math without you like coffee without sugar .. :) thanks and keep going
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
This is the best explanation. You explain the concept clearly. Thank you so much
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
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
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!
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
this video makes me want to burn my calculus book
Thanks! I'm a big fan of your teaching style.
Thank you very much for this beautiful explanation! It's helped me a ton in understanding double integrals!!! 😍
Glad it was helpful, Ishaan!
Great video ! Thanx for taking the time out for this. :)
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!
so so so happy i found this!!! LIFE SAVING
+Cesar Solorzano I'm so glad it could help!
You explain things much more succinctly than any of my past teachers/lecturers :)
Thank you very much!
You’re the best calc explainer yet
Krista is the Queen of Math!
Can't live without Krista during coronavirus thank u so much
You're welcome, Chen! Hope you and your family are safe and healthy! :)
The best explanation I’ve seen so far. Superb! Wish you were my lecturer
I'm so glad you liked the video! :D
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!!
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. :)
Glad I could help! :)
You are really amazing. Thanks for providing free lectures.
My pleasure, Dawlad! I'm happy I'm able to 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.
I am no longer lost, thank you so much!!
Glad it could help!
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!!
Your tutorial is still live here, thanks for the wonderful explanation you got my finger
Aww thanks! You too! :)
Have you any video with upper limit and lower limit given in any Polar integration?
This is so much better than the way my teacher explained it, or at least tried to.... Thanks!
You're welcome, glad it helped!
i always get stuck while solving this problem, but i had almost mastered it. Once again THANK YOU very much.
Hi @krista - Is the final answer correct ? Actually, the limit of "u" was not included in the integral. You continued the integral calculations with the limits of r only. limits of u will be 0 to 4
she immediately plugged r^2 back into u, so you dont need to convert the bounds to u
true
Ya
It's true
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
Thank you mam it is very easy to learn from your videos rather than from class
You're welcome!
What a coincidence! I was stuck at this problem when I decided to check your video for help.
Thanks. I've been trying to understand Maxwell's equations and the vids on double integrals has been helpful
She’s the best teacher ever
Oh thank you! You saved my time and life. I am grateful to you
awesome! i'm so glad!! :)
but why does dxdy become drdø multiplied with r?
I cover that in my video on double integrals in polar coordinates.
It's the determinant of the Jacobian.
it the 'jacobian' which is just a scaling factor when you change from the cartersian cord. to polar coordinate
so when you integrate r you get r^2/2 Surfaces are length measurements, (r), squared.
probably the best video out there of explaining this example!!!
Thanks! :)
can't beat it! :)
thank you so much you're such a great teacher
Thank you big sister , my doubts were regarding ,that how to take theta, which is cleared in one example , thank you for your help🙏🙏
Just a few hours before my exam, you are a life saver🙏
I hope the exam went great! :D
Ohhhh, the good ole multi calc days. Probably the best calculus there is!!!
You're welcome!
You make it look so easy!!! Thank you so much for your videos!!!!
You are simply the best! Thank you!
Wonderful explanation, thanks!
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.
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 😊
Thanks! you have no idea how much trouble i had to understand this before.
You're welcome! I'm so glad it helped!
Thanks a lot !! Made this much clearer !
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
Excellent explanation! Really thankful for the clear example.
Thanks! I'm glad it could help!
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.
That was awesome, Thanks! Helped me understand stuff for my exam :)
So glad I could help! :D
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
Great video! Thank you so much krista!
+Praful Kamdar You're welcome, Praful!
Much better than my teacher! Thanks soo so much!
Very clear explanation. Thanks
You're welcome, I'm glad it made sense! :)
This video helped me so much. Thank you so much!!!!!!!
You're welcome! Glad it could help!
super clear. easy to understand every step. thanks.
You're welcome! :D
Krista King why didn’t you change the limit after u get U instead r^2
this video was too helpful for me thank you for publishing this video
+Vignesh Adithyan Glad I could help!
you made it look very easy . Thanks alot , it helped . 🙏
Glad it could help!
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!
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! :)
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! :)
Nice and clear explanation!
Thanks!
Wow, that was immensely thorough. Thank you!
You're welcome!
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! :)
Thank you so mucch!! You are an excellent teacher!! Love you!! :)
Awww thank you so much, I'm happy to help! :D
Awesome video, right on the topic I needed to review!
Hi, isn't the o-2 bounds suppose to change to 0-4 when using the u-substitution
I LOVE YOU LOVE YOU LOVE YOU LOVE YOU, U JUST SAVED MY ASS BIG TIME xDDD
i have final exam tomorrow and i didn't understand anything about this subject, and was about to give up after watching every video possible, then i saw this video and thought to give it 1 last try before i drop calculus3, AND I'M SO GLAD I WATCHED IT, THANK U
+Hosam Hassan Awww thank you so much! I'm so glad that the video helped and that you decided not to drop the class. Good luck on your final, I hope it goes great!!
+Krista King | CalculusExpert.com thank u so much :)
very well explained madam..calculus with your sweet voice..its like icing on cake..;-)
+Amit Kumar Thank you very much!