Converting iterated integrals to polar coordinates (KristaKingMath)

► My Multiple Integrals course: www.kristakingmath.com/multip...
Learn how to convert iterated integrals from cartesian coordinates to polar coordinates.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@kristakingmath]

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

[@celsiusfahrenheit1176]

Thank you Krista for taking the time to explain.

[@wahidhamidy6886]

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

[@AaronFu]

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

[@vickykong5868]

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]

Thanks! Good luck on your final!

[@SSawhney]

Really nice video, I love how you break the question up so its nice and simple. :)

[@kristakingmath]

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

[@kristakingmath]

I explain here :) integralcalc . com/how-I-create-my-videos

[@ballwizz23]

I understand! Thank you so much, you helped me pass this class!

[@13.r.rrahul]

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

[@MaritzaRoche]

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

[@TalhaStudios]

Krista U really are a KING

[@kristakingmath]

You're so welcome! :)

[@ThePinoyMamba]

awesome Voice! just made my day! Thanks Krista!

[@Escap1st7]

Brilliant video. Cleared everything for me.

[@trinistylez2345]

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]

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

[@cielomartos7807]

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]

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

[@nicksterwixter]

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

[@TheDanischannel]

Absolutely in love with this! Life saver.

[@kristakingmath]

+TheDanischannel I'm so glad it helped!

[@mirzamunir2904]

Easy to understand! Thank you so much 😊

[@kristakingmath]

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

[@kristakingmath]

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

[@Anon_life]

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

[@kristakingmath]

So glad they're helping! :)

[@rykezarr9502]

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

[@kristakingmath]

Awesome, thank you, Ryke! :)

[@wenqingtoh852]

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]

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

[@amalalshehri5312]

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

[@geraldaoi7645]

This really helped me out. cheers

[@JustinTulsiram]

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]

So glad I could help!

[@147258369572]

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]

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

[@yvonnerodriguez8336]

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

[@mathambojere8914]

thank you so much, the explanation was clearly

[@kristakingmath]

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

[@mayankjha8832]

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]

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

[@jessestroster7687]

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

[@md.nazmulhassan9505]

Thank you so much.

[@nubsmacker]

This was extremely helpful, thank you!

[@kristakingmath]

Thanks for letting me know! :)

[@VasileSurdu]

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

[@buhlerasimeni9471]

it is clear and straight forward

[@cameronfranchi9284]

thanks so much, vivid explanation!

[@kristakingmath]

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

[@ahmadmax4478]

I appreciate your effort. Thanks again:)

[@kristakingmath]

You're welcome! :)

[@saadsalman8386]

That was some great explanation... thanks!

[@kristakingmath]

you're welcome!

[@isabelhazan6546]

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

[@kristakingmath]

Thanks! :D

[@shihabchowdhury2707]

you are the best .really love the way u teach

[@kristakingmath]

Glad you like it!

[@janaawada3741]

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

[@sofiarossi1906]

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]

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

[@haftamutadele3751]

you are my hero thanks,,, krista king

[@csbnikhil]

The Colors used are very helpful, perfectly explained.

[@kristakingmath]

+Nikhil CSB Thanks!

[@surajahire744]

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

[@eddylee6691]

This helps a lot.Thank you

[@kristakingmath]

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

[@Steerwithsvm]

Thanks a lot for such a good explanation :)

[@kristakingmath]

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

[@kristakingmath]

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!! :)

[@emrearslan1797]

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]

+Emre Arslan Awww thank you so much!

[@karanbhanushali6756]

Nice explanation

[@roryh2241]

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

[@kristakingmath]

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

[@kristakingmath]

Aw thanks! :D

[@gikihacker2185]

THANKS!

[@barcamsn7836]

Thank you very much explain the wonderful

[@kristakingmath]

+Barca MSN You're welcome!

[@fungusthemungus3754]

OMG! LIFE SAVER!

[@fikret8422]

thank you

[@JM995able]

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

[@kristakingmath]

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

[@kristakingmath]

Glad you liked it! :)

[@mustafamerrick7975]

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[@jaxonheath3038]

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

[@emmittparker549]

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

[@adrielmarley3284]

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

[@arijohan3511]

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

[@plaxen1]

Amazing, thank you

[@kristakingmath]

+Martin Mikitas You're welcome!

[@salmanhameed847]

thankyou very much it was very helpful

[@kristakingmath]

Glad it could help!

[@EslamMohamedX]

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

[@kristakingmath]

+Eslam Mohamed Thank you so much!

[@kristakingmath]

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. :)

[@rlg6728]

Thx alot for the video this was very helpful

[@kristakingmath]

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

[@mulanganekhwalivhe662]

thanks, god bless you

[@subodhadhikari8489]

Thanks

[@kristakingmath]

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! :)

[@muwongeevanspaul9166]

Thanks king

[@user-ot8pb2tb9e]

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

[@AznProful]

My savior!!!

[@RaviRahulKumarShah]

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

[@huihui666]

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.

[@imadliani6215]

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

[@kristakingmath]

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

[@NK-iy6if]

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

[@kristakingmath]

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

[@jjsanchez927]

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

[@slave2truth4freedom]

THANK YOU

[@kristakingmath]

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

[@LALO365]

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

[@kristakingmath]

+LALO365 Glad I could help!

[@Ezrik2006]

your amazing!

[@kristakingmath]

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

[@mhmdmansor5163]

great job

[@kristakingmath]

Thanks!

[@ahmeraymen2006]

thanks make my life so easy

[@kristakingmath]

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

[@jgc9199]

Thanks! By the 5 minute mark everything from class clicked in lol.

[@kristakingmath]

Oh good! I'm so glad it made sense! :)

[@allstarshotta]

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

[@franciscomendez9327]

You're awesome! Haha, thank you so much

[@kristakingmath]

+Francisco Mendez You're welcome, happy to help!!

[@Daan87423]

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

[@MuhammedSami]

thax alot you save me

[@kristakingmath]

you're welcome! :D

[@escarlai]

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

[@ferozahmedsoomro]

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]

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

[@089jitendraseervi2]

Make more video on polar coordinate changes

[@TheChesster777]

wish I knew this channel existed before the semester started haha...

[@omarseraj5917]

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

[@lucypham7950]

I love you!!!

[@kristakingmath]

Right back at ya!

[@ashidilkhan]

looking nine in New DP

[@hamsack981]

god damn, she is amazing!

[@hg2.]

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

[@tonyten8912]

Amazing

[@kristakingmath]

Thanks, Munashe! :)

[@theodoreberbach9562]

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

[@kristakingmath]

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.

[@sithumkarandawala4502]

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

[@andrewmcdowell8158]

very helpful thank you, wish you were my professor. I'm sure many others would agree XD

[@bArda26]

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