Thank you Krista for taking the time to explain.

best video on iterated integral so far. You even included you substitution. Thank you very much.

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 !

@kristakingmath

7 жыл бұрын

Thanks! Good luck on your final!

The best video of changing cart. integral to polar integral i 've found on youtube! i appreciate your effort miss!

thank you very much! i'm so glad the videos are helping!! :)

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!

Krista U really are a KING

Brilliant video. Cleared everything for me.

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!.:)

@hamzamohammadnawaz

7 ай бұрын

you've probably made it by now..im in calc 3 rn :(

these videos are so amazing nd simple to understand..!

awesome Voice! just made my day! Thanks Krista!

Your videos are awesomeee! :) Thank you so much!

Absolutely in love with this! Life saver.

@kristakingmath

8 жыл бұрын

+TheDanischannel I'm so glad it helped!

You are AMAZING! Thanks so so much for the help!

Easy to understand! Thank you so much 😊

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.

@kristakingmath

4 жыл бұрын

Thank you so much, Cielo! I'm so glad the videos have been helping! :D

You definitely are the KING, thank you for your videos :)

@kristakingmath

6 жыл бұрын

So glad they're helping! :)

you're welcome!! hope you're having a great summer!! :)

You were really helpful can u post with more examples Thank you

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

this was the most helpful example i came across today! you rock!

@kristakingmath

4 жыл бұрын

Awesome, thank you, Ryke! :)

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.

@kristakingmath

9 жыл бұрын

So glad I could help!

@147258369572

9 жыл бұрын

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

@RealationGames

9 жыл бұрын

saleh ali Nope, it's the area. This is 2 dimensional function, not 3 dimensional.

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..

@kristakingmath

8 жыл бұрын

Thank you so much! Good luck with your exams, and I hope you enjoy the rest of the videos!

Thank you so much for clearing my doubt on how to calculate the theta value which had bothered me for so long!! Thank you!!!!

@kristakingmath

6 жыл бұрын

You're welcome, I'm so glad it helped! :)

This really helped me out. cheers

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.

Thank you so much Krista King .. Help me thank you

tnx a LOT, you explain very easy/detailed and your voice is nice. tnx ;)

i hope they help, and good luck on your test!! :D

you are the best .really love the way u teach

@kristakingmath

7 жыл бұрын

Glad you like it!

This was extremely helpful, thank you!

@kristakingmath

10 жыл бұрын

Thanks for letting me know! :)

thanks so much, vivid explanation!

@kristakingmath

7 жыл бұрын

You're so welcome! I'm glad you liked it. :D

That was some great explanation... thanks!

@kristakingmath

9 жыл бұрын

you're welcome!

3:33 should be "entire half circle that is above x-axis " or ?

thank you so much, the explanation was clearly

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 !!!

@kristakingmath

8 жыл бұрын

+Emre Arslan Awww thank you so much!

The Colors used are very helpful, perfectly explained.

@kristakingmath

8 жыл бұрын

+Nikhil CSB Thanks!

it is clear and straight forward

This helps a lot.Thank you

@kristakingmath

8 жыл бұрын

+eddy lee You're welcome, I'm so glad it helped!

I appreciate your effort. Thanks again:)

@kristakingmath

10 жыл бұрын

You're welcome! :)

This video was amazing. Thank you!!!!!

@kristakingmath

7 жыл бұрын

Thanks! :D

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 :)

@kristakingmath

5 жыл бұрын

I'm so glad it helped, Celestial! Thanks for letting me know! :D

You're so welcome! :)

thanks! i'm glad you liked it!! :D

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!! :)

Do you have any videos regarding integrals in cylindrical and spherical coordinates???

you are my hero thanks,,, krista king

Thank you so much! I forgot everything the next day when I actually tried to do my homework!

Thanks a lot for such a good explanation :)

@kristakingmath

8 жыл бұрын

+The Unofficials You're welcome, I'm so glad it helped!

Nice explanation

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

The only thing that I can say is THANK YOU, you saved my day :)

@kristakingmath

9 жыл бұрын

You're welcome, I'm so glad it helped!!

since you are substituing u, shouldnt the range of u goes from zero to 9 since u = r^2 ?

@kristakingmath

7 жыл бұрын

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.

OMG! LIFE SAVER!

Thank you a lotttt please do more examples about two intersecting circles

thank u so much....my all douts are clear...❤😘😍😍😍😍😍❤

Your reasoning is perfectly logical. You make everything look zillion times simpler.

@kristakingmath

8 жыл бұрын

+Eslam Mohamed Thank you so much!

Do you have any vid where you use pts (x,y,z) to find surface area?

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! :)

6:48 What if it's dxdy? Do you need to turn them around first?

I had a problem just like this I had to figure out! Thanks so much!

@kristakingmath

4 жыл бұрын

You're welcome, Rory! I'm so glad it helped! :)

NICE,,JUST NEED 10 MIN TO STUDY. THERE IS BETTER THAN MY TEACHER TEACHING 2 HR..orz

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?

@kristakingmath

3 жыл бұрын

Hi Tianhong! I use Sketchbook, which is made by Autodesk. :)

Do you have more videos explaining this or a nice website please put it in description

You've helped me a lot. Greetings from Mexico city.

@kristakingmath

8 жыл бұрын

+LALO365 Glad I could help!

My savior!!!

Isn't the answer should be pi/2 (1-sin9)? double integration of sin is still sin right?

3:24 If the limits of integration for x had been -2 to 2, how would you define your limits of integration for r and theta? I have a problem like that for homework, but I don't know if I am supposed to be using polar (or how to use polar for that).

@ZeekCannon

8 жыл бұрын

+xcrunner 0 to 2pi since you want the whole circle

Thank you very much explain the wonderful

@kristakingmath

8 жыл бұрын

+Barca MSN You're welcome!

There's Chain Rule "hidden" in the r substitution for sin(r^2) right?

Amazing, thank you

@kristakingmath

8 жыл бұрын

+Martin Mikitas You're welcome!

I have a question at 8:40 don't we have to change the integral limits?

Thx alot for the video this was very helpful

@kristakingmath

3 жыл бұрын

You're welcome, Robert! I'm so glad it helped! :)

thankyou very much it was very helpful

@kristakingmath

7 жыл бұрын

Glad it could help!

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...

@ZeekCannon

8 жыл бұрын

+Luca Capobianchi In that case you wouldnt use polar coordinates lol

Feel better after 20 mins of your videos compared to hours of class time and studying on my own

@kristakingmath

4 жыл бұрын

I'm so glad the videos are helping! :D

THANKS!

thanks, god bless you

thank you so much we need more exemples and please if you can the triple integral

@kristakingmath

8 жыл бұрын

+imad liani You're welcome, and I will definitely continue to add more videos.

thank you

what if the differentials were dxdy would you still use the same format or would you switch them and make it r dr d(theta)?

@kristakingmath

7 жыл бұрын

You would keep everything exactly the same, except the limits of integration would be switched. So you'd still replace dx dy with r dr d(theta). You'd still replace the original integrand with sin(r^2). But because the order of integration was different, instead of int [0,pi] int [0,3], you'd end up with int [0,3] int [0,pi]. I hope that helps!

God bless youuu!!! Thank you so much!!!

@kristakingmath

2 жыл бұрын

You're welcome, I'm happy to be able to help! :)

thank you!!! krista 2016. I'm with her

Silly question - what is the difference between an iterated and a double integral (if any)?

Thanks king

If it is cos in place of sin,what is the outer integral limits

When you went into the "u-universe(as my great high school calculus teacher called it), and made u = r^2... Shouldn't the limits chang? So 0 would remain the same because (0)^2= 0... But the higher limit 3 would turn into 9 because (3)^2 equals 9...? So the new limits of integration should be from 0 to 9...right? Or am I being dumb?

@kristakingmath

9 жыл бұрын

jesus moreno you're not being dumb. i didn't change them because i was planning to back-substitute so that i could evaluate with respect to the original variable. but i should have indicated at that step that the limits were still related to the original variable. if you're not planning to back-substitute, then yes, you definitely have to change them so that the limits of integration are in terms of u, instead of r.

your amazing!

@kristakingmath

3 жыл бұрын

Thank you so much, Shawn! I'm glad you liked the video! :)

Darling would you be kind enough to tell ,e what app and device you use to make these videos?

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))

@kristakingmath

8 жыл бұрын

+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.

@ShareInfos516

8 жыл бұрын

+Krista King | CalculusExpert.com That's correct.

Glad you liked it! :)

@mustafamerrick7975

3 жыл бұрын

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@jaxonheath3038

3 жыл бұрын

@Mustafa Merrick definitely, been using Kaldrostream for since november myself :D

@emmittparker549

3 жыл бұрын

@Mustafa Merrick Definitely, been using Kaldrostream for months myself =)

@adrielmarley3284

3 жыл бұрын

@Mustafa Merrick Yup, been using kaldroStream for months myself :)

@arijohan3511

3 жыл бұрын

@Mustafa Merrick yup, I have been using Kaldrostream for years myself :D

Thanks

thanks make my life so easy

@kristakingmath

4 жыл бұрын

You're welcome, farrukh! I'm so glad it helped!

great job

@kristakingmath

8 жыл бұрын

Thanks!

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?

god damn, she is amazing!

THANK YOU

@kristakingmath

8 жыл бұрын

+Keoni Fleming You're welcome! Glad you liked it.

At 9:20, shouldn't that have been -1/2 sin(9)?