NOT a silly question at all! :) The difference is that a double integral doesn't specify the order of integration, and you'll see integral notation like (\int\int)_R, which tells you that you're integrating over the region R, but doesn't tell you whether you should integrate first with respect to x or y. An iterated integral has already done the work for you and tells you the order of integration. You'll see integral notation like \int_0^1\int_-2^2. Hope that helps!! :D
seriously you are very good......in all those year's I was always lack behind with basics....now you saved my life...after completing my exams. ..I will cover your all lectures...then move ahead. ...Thank you...you have very good ability to teach..
no, because cos(9) is a constant. multiply that by -1/2, and you still have a constant. so you really have to look at that whole term, -1/2 cos(9), as a constant, just like if it were just 3, or 7. if you took the integral of 3, you'd get 3\theta, which means the integral of -1/2 cos(9) is (-1/2 cos(9))\theta. great question, and i hope that helps!! :)
I know this was made in 2013 and you probably aren't looking at comments, but on the off chance that you do, thank you a lot for this video!! It was very clear and helped me a lot :)
LOL, I totally understand!! :) Unfortunately I'm going to have to ask you to ignore me for a few months, because I need to get these videos out so that they can help people in summer school, and so that they're ready for the fall when everybody gets back to school! :)
The reason I didn't change the limits of integration is because I was planning to back-substitute for r before I evaluated over the interval. If you want to leave the function in terms of u, then you need to change the limits of integration so that they correspond to u. But if you back substitute and put the function back in terms of r, then you'd just need to change the limits of integration back anyway, so I didn't change them. :)
hey love your teaching 10:25 is it really the area of that circle or is it the volume of some soild where its projection is the region represented by the circle i am not sure about the latter but pretty sure that the answer in not the area of that circle please explain love your videos thanks
integralCALC It was pretty rough but this stuff- I did well on.Hopefully there is a curve and I can keep my B+ haha You were really helpful though, I have you right there with PatrickJMT on the most helpful videos for Calculus!
Yes, but I knew I was going to back-substitute at the end of the problem, which is why I didn't bother. After back-substituting, I would have had to change the limits back to what they were originally.
+TES HAI No, cos9 doesn't need to be integrated. cos9 is a constant, so when you integrate with respect to theta, you'd get (cos9)(theta). If you have cos(x), then you need to integrate, but cos of a constant is a constant, so it doesn't change like you're saying.
Hi Krista. Your videos are super useful. I like the presentation. I wanna know which software do you use which has black board like background and a nice cursor?
I have a question. You know how you found the new limits of integration in polar coordinates geometrically by drawing a picture? Is there a way to find the limits of integration analytically like how you substituted r^2 into the integrand? I can't seem to find a way to do it analytically.
So what if we were to tweak the bounds for example? Say from y = x to y = sqrt(9 - x^2) and from 0 to 1? I am curious as to what the picture would look like and how we would set up bounds for that...
When r = 0 => u = 0, but when r = 3 => u = sqrt(3). But you kept the boundaries of integration from 0 to 3. I don't understand. Can you answer me please?
NOT a silly question at all! :) The difference is that a double integral doesn't specify the order of integration, and you'll see integral notation like (\int\int)_R, which tells you that you're integrating over the region R, but doesn't tell you whether you should integrate first with respect to x or y. An iterated integral has already done the work for you and tells you the order of integration. You'll see integral notation like \int_0^1\int_-2^2. Hope that helps!! :D
The final is just around the corner and I was glad to find your video. It works perfectly for me. Clear voice and steps. Keep it up !
Thanks! Good luck on your final!
seriously you are very good......in all those year's I was always lack behind with basics....now you saved my life...after completing my exams. ..I will cover your all lectures...then move ahead. ...Thank you...you have very good ability to teach..
Thank you so much! Good luck with your exams, and I hope you enjoy the rest of the videos!
no, because cos(9) is a constant. multiply that by -1/2, and you still have a constant. so you really have to look at that whole term, -1/2 cos(9), as a constant, just like if it were just 3, or 7. if you took the integral of 3, you'd get 3\theta, which means the integral of -1/2 cos(9) is (-1/2 cos(9))\theta. great question, and i hope that helps!! :)
Thank you Krista for taking the time to explain.
Your reasoning is perfectly logical. You make everything look zillion times simpler.
+Eslam Mohamed Thank you so much!
I know this was made in 2013 and you probably aren't looking at comments, but on the off chance that you do, thank you a lot for this video!! It was very clear and helped me a lot :)
I'm so glad it helped, Celestial! Thanks for letting me know! :D
thank you very much! i'm so glad the videos are helping!! :)
I can not say this enough but thank you. You are the only reason I am doing so well in calc 3!!!!! Please keep doing what you do.
Thank you so much, Cielo! I'm so glad the videos have been helping! :D
you're welcome!! hope you're having a great summer!! :)
best video on iterated integral so far. You even included you substitution. Thank you very much.
You are amazing!!..Im doing these stuff right now in Calc 3 and you teach and explain these topics so well..keep up the great work!.:)
you've probably made it by now..im in calc 3 rn :(
Thank you so much for clearing my doubt on how to calculate the theta value which had bothered me for so long!! Thank you!!!!
You're welcome, I'm so glad it helped! :)
The Colors used are very helpful, perfectly explained.
+Nikhil CSB Thanks!
The best video of changing cart. integral to polar integral i 've found on youtube!
i appreciate your effort miss!
You were really helpful can u post with more examples
Thank you
You're so welcome! :)
Krista U really are a KING
thanks! i'm glad you liked it!! :D
You definitely are the KING, thank you for your videos :)
So glad they're helping! :)
Glad you liked it! :)
a tip : you can watch series at kaldroStream. Been using them for watching lots of of movies recently.
@Mustafa Merrick definitely, been using Kaldrostream for since november myself :D
@Mustafa Merrick Definitely, been using Kaldrostream for months myself =)
@Mustafa Merrick Yup, been using kaldroStream for months myself :)
@Mustafa Merrick yup, I have been using Kaldrostream for years myself :D
this was the most helpful example i came across today! you rock!
Awesome, thank you, Ryke! :)
LOL, I totally understand!! :) Unfortunately I'm going to have to ask you to ignore me for a few months, because I need to get these videos out so that they can help people in summer school, and so that they're ready for the fall when everybody gets back to school! :)
Absolutely in love with this! Life saver.
+TheDanischannel I'm so glad it helped!
I know I am saying always the same thing that you are awesome for your each video but I can't stop myself YOU ARE AWESOME !!!
+Emre Arslan Awww thank you so much!
i hope they help, and good luck on your test!! :D
Your videos make learning all this stuff so easy! Thank you so much for these, you've helped me do well on my final exam.
So glad I could help!
integralCALC thanks for that but in the end of the video you say it is the area but i think it is the volume of the function
saleh ali
Nope, it's the area. This is 2 dimensional function, not 3 dimensional.
Brilliant video. Cleared everything for me.
The only thing that I can say is THANK YOU, you saved my day :)
You're welcome, I'm so glad it helped!!
it is clear and straight forward
Really nice video, I love how you break the question up so its nice and simple. :)
I understand! Thank you so much, you helped me pass this class!
these videos are so amazing nd simple to understand..!
The reason I didn't change the limits of integration is because I was planning to back-substitute for r before I evaluated over the interval. If you want to leave the function in terms of u, then you need to change the limits of integration so that they correspond to u. But if you back substitute and put the function back in terms of r, then you'd just need to change the limits of integration back anyway, so I didn't change them. :)
thank you so much we need more exemples and please if you can the triple integral
+imad liani You're welcome, and I will definitely continue to add more videos.
Thank you a lotttt please do more examples about two intersecting circles
You've helped me a lot. Greetings from Mexico city.
+LALO365 Glad I could help!
Easy to understand! Thank you so much 😊
hey love your teaching
10:25 is it really the area of that circle or is it the volume of some soild where its projection is the region represented by the circle
i am not sure about the latter but pretty sure that the answer in not the area of that circle
please explain
love your videos
thanks
3:33 should be "entire half circle that is above x-axis " or ?
Do you have any videos regarding integrals in cylindrical and spherical coordinates???
you are the best .really love the way u teach
Glad you like it!
I had a problem just like this I had to figure out! Thanks so much!
You're welcome, Rory! I'm so glad it helped! :)
Thank you so much Krista King .. Help me thank you
A life saver T-13 hours before my Calculus 3 Final!
teleton11 Good luck on your final, I hope you do great!!
integralCALC It was pretty rough but this stuff- I did well on.Hopefully there is a curve and I can keep my B+ haha
You were really helpful though, I have you right there with PatrickJMT on the most helpful videos for Calculus!
integralCALC BTW, just curious- what is your math education?
teleton11 Thank you very much! I hope there's a curve too!
integralCALC I didn't study math, I've just been a tutor for a long time.
That was some great explanation... thanks!
you're welcome!
thanks so much, vivid explanation!
You're so welcome! I'm glad you liked it. :D
awesome Voice!
just made my day!
Thanks Krista!
NICE,,JUST NEED 10 MIN TO STUDY.
THERE IS BETTER THAN MY TEACHER TEACHING 2 HR..orz
thank you so much, the explanation was clearly
You are AMAZING! Thanks so so much for the help!
Nice explanation
This was extremely helpful, thank you!
Thanks for letting me know! :)
since you are substituing u, shouldnt the range of u goes from zero to 9 since u = r^2 ?
Yes, but I knew I was going to back-substitute at the end of the problem, which is why I didn't bother. After back-substituting, I would have had to change the limits back to what they were originally.
Thank you so much! I forgot everything the next day when I actually tried to do my homework!
Isn't the answer should be pi/2 (1-sin9)? double integration of sin is still sin right?
This helps a lot.Thank you
+eddy lee You're welcome, I'm so glad it helped!
tnx a LOT, you explain very easy/detailed and your voice is nice.
tnx ;)
This really helped me out. cheers
Do you have more videos explaining this or a nice website please put it in description
you are my hero thanks,,, krista king
Great video!! I just want to mention that you forgot to integrate second integral at the end. It should be Pi/2(1-sin(9))
+TES HAI No, cos9 doesn't need to be integrated. cos9 is a constant, so when you integrate with respect to theta, you'd get (cos9)(theta). If you have cos(x), then you need to integrate, but cos of a constant is a constant, so it doesn't change like you're saying.
+Krista King | CalculusExpert.com That's correct.
This video was amazing. Thank you!!!!!
Thanks! :D
I love your videos but can u slow down with the videos during summer break?! Lol im really not tryna see calc in my subscription list lol
Your videos are awesomeee! :) Thank you so much!
There's Chain Rule "hidden" in the r substitution for sin(r^2) right?
Hi Krista. Your videos are super useful. I like the presentation. I wanna know which software do you use which has black board like background and a nice cursor?
Hi Tianhong! I use Sketchbook, which is made by Autodesk. :)
thank you!!! krista 2016. I'm with her
Thank you so much.
thank u so much....my all douts are clear...❤😘😍😍😍😍😍❤
Thank you very much explain the wonderful
+Barca MSN You're welcome!
Aw thanks! :D
I have a question at 8:40 don't we have to change the integral limits?
I appreciate your effort. Thanks again:)
You're welcome! :)
Silly question - what is the difference between an iterated and a double integral (if any)?
Do you have any vid where you use pts (x,y,z) to find surface area?
I have a question. You know how you found the new limits of integration in polar coordinates geometrically by drawing a picture? Is there a way to find the limits of integration analytically like how you substituted r^2 into the integrand? I can't seem to find a way to do it analytically.
thankgod you dont have a robotic voice like other similar tutorials
Make more video on polar coordinate changes
Thanks a lot for such a good explanation :)
+The Unofficials You're welcome, I'm so glad it helped!
thanks, god bless you
Thanks! By the 5 minute mark everything from class clicked in lol.
Oh good! I'm so glad it made sense! :)
thank you
So what if we were to tweak the bounds for example? Say from y = x to y = sqrt(9 - x^2) and from 0 to 1? I am curious as to what the picture would look like and how we would set up bounds for that...
+Luca Capobianchi In that case you wouldnt use polar coordinates lol
Darling would you be kind enough to tell ,e what app and device you use to make these videos?
THANK YOU
+Keoni Fleming You're welcome! Glad you liked it.
thanks make my life so easy
You're welcome, farrukh! I'm so glad it helped!
6:48 What if it's dxdy? Do you need to turn them around first?
Amazing, thank you
+Martin Mikitas You're welcome!
When r = 0 => u = 0, but when r = 3 => u = sqrt(3). But you kept the boundaries of integration from 0 to 3. I don't understand. Can you answer me please?
Thanks, now I won't fail my test tomorrow :')
+Minh Tri I hope it goes well!
very helpful thank you, wish you were my professor. I'm sure many others would agree XD
thankyou very much it was very helpful
Glad it could help!
Thanks
If it is cos in place of sin,what is the outer integral limits
THANKS!
At 9:20, shouldn't that have been -1/2 sin(9)?
is this calculus 1? cause im having this class next year in cegep
OMG! LIFE SAVER!
Thx alot for the video this was very helpful
You're welcome, Robert! I'm so glad it helped! :)