Double polar integral to find the volume of the solid (KristaKingMath)

► My Multiple Integrals course: www.kristakingmath.com/multip...
Learn how to use a double polar integral to find the volume of the solid.
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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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[@michaeljcarn]

You're so good at explaining. If only you could explain to my professors how to properly teach calculus lol

[@kristakingmath]

I'm glad I can at least help through the videos. :)

[@hg2.]

.... They'd be out of a job... ha ha. All that tuition you pay and Krista runs circles around them :)

[@raba2d723]

@@hg2. in polar coordinates!

[@hg2.]

@@raba2d723 4 years? That long? I haven't checked in with Krista for a good while (understatement), I headed for Physics-w-calculus, and Nuclear-Engineering-101-Berkeley. No - I didn't understand a lot of it, but Krista got me up and running on the math enough to hang in for the course lectures. Never once put pencil to paper -- LOL. Not exactly setting a good example, but it's a just a hobby. Thank you Krista!

[@laimino]

You've helped me so much in my calculus college classes ( calculus 1,2 &3). I'm so grateful. I can't say thank you enough .

[@kristakingmath]

You're welcome, laimino! I'm so glad I've been able to help along the way! :)

[@nitishchauhan8655]

What helped me understand the r boundaries was that you look for the intersection of the two boundary graphs. so z = 2 and other combine to make 4 = 1 + x^2 + y^2. After you substitute the values of x and y with polar coordinates you have a function of r. The range of this function of r gives you the boundaries (r>=0). In the video you told me what I was doing but not why (2:29). Thanks for the video though, great help!

[@ilovesudan]

Brilliant, Thanks!

[@eduardo0796]

Excellent explanation. Another way to do the u substitution is by evaluating what you equal u to with the limits of integration, for example if u = 1+r^2 and your limits of integration are 0 and sqrt(3), you evaluate that in u, getting 1 and 4 as the new limits of integration and that way you can evaluate the result of the integration.

[@kristakingmath]

Hi! Glad you like it! I explain the process here :) integralcalc . com/how-i-create-my-videos/

[@pabloalbarran7572]

Awesome job with these videos :3

[@mervealpay2671]

your explaining is very clearly, thanks a lot for your videos

[@kristakingmath]

Thank you! I'm glad you like them. :)

[@ivangong7554]

Thank you extremely

[@AaronFu]

ur officially my favorite person . Calc quiz in7 hrs, might pull all nighter i dunno. I wish I found you earlier.

[@pedrovilaca3291]

OMG! It was the exact exercise that I was having problems with! THANKS!!!!

[@kristakingmath]

+Pedro Vilaça You're welcome!

[@xxegyzz5250]

I always run to this channel when my professors didn't explain clearly how they come up with their solution. Thanks a lot hope those adds and liking your videos could help.

[@kristakingmath]

I'm so glad my videos can help fill the gap... thanks for letting me know that they're helping! :)

[@buddydog1956]

far out!!! great vid!!!

[@Neueregel]

thx for sharing

[@PortugalOle10]

THANK YOU

[@kristakingmath]

Aww James c'mon!! This isn't too hard, you can totally do it! ;)

[@TheRaja00786]

Thanks a lot Krista.. u have taught this very well... Before watching Ur video that wasn't my cup of tea.. bt now I'm very happy and satisfied .. thanku once again 🙋🙋

[@kristakingmath]

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

[@kristakingmath]

Hope it went well! :D

[@evaristogabriel8208]

IT WORKEDDDDDD

[@kasansaronald8337]

this has been like super awesome thanx a lot

[@kristakingmath]

You're welcome, Kasansa, I'm so glad you liked it! :)

[@MrShakingcold]

can you please tell me the applications of double integral in engineering?

[@astridolofsson395]

Why do we subtract sqrt(1-r^2) from 2? I need to understand why before I can apply it. I really appreciate your videos =)

[@guitarttimman]

Great job. As a suggestion, you should add that the answer is actually 4 pi/3 cubic units because it's a volume.

[@gabrielsiles1958]

thank you my lady

[@SusanCastillo-fz4iw]

amazing

[@josejimenez850]

thank you!

[@kristakingmath]

:D

[@troivayha512]

OMG TY SO MUCH!!

[@kristakingmath]

You're very welcome!!

[@minkmonk897]

Where did 2 - sqrt (1+r^2) come from? Isn't the function to be evaluated sqrt. (1+r^2)?

[@neema_]

amazing! easy to understand :)

[@kristakingmath]

+Estherr Barak I love that feedback! Exactly what I'm hoping for. :)

[@ganeshsasidharan5278]

+CalculusExpert.com YOU THE REAL MVP

[@360xi]

ughhhhhhhhhhhhhhhhhh I have a similar problem just like this one. I was so happy cause I thought since they were similar I would get it but nope. Mine is " Find the area of surface. S is the part of the sphere x^2 + y^2 + z^2 = 9 that lies above the plane z=2." I obtain the answer (8/3)pi but the book says the correct answer is 6pi.

[@actuary32174]

What program did you use to produce this video? I also teach math on-line and like this type of presentation.

[@0796675465]

We could make the integral (1+r^2)^(.5) - 2 and if we had a negative answer we reverse it to the positive answer

[@peterlee5726]

Is it possible to solve this using a triple integral? and just have z be one of the bounds of integration?

[@mathewdominguez8967]

isnt the integral of (x)^1/2 = (2(x)^3/2)/3?

[@fabo2268]

Why do you substract 2-(sqr1+r2) in min 5:24 apox. Thank you, good videos.

[@shapedsilver3689]

Does anybody know the answer to this? I don't get it either, it seems arbitrary

[@Shaiifalii]

Look here we're finding the volumne under z=2 line So the height of the volume will be: Total ht (z=2) - total ht of sphere (z in terns of x,y)

[@ahmadalfaisal4132]

Very useful, thanks :-)

[@kristakingmath]

:D

[@Ensign_Cthulhu]

Hang on, why can't you have a negative r? Isn't this just the same as a positive r flipped through pi radians?

[@thekingsjester0]

Yes, technically that's true, but using a negative r value isn't helpful in this context.

[@MrWester22]

How do you know that you are dealing with the full circle (2pi) ?

[@Shaiifalii]

It's a sphere with centre on origin so 2 pie

[@SiamData]

How is it a volume integral if there is only two integral?Plz help me out

[@jiteshdeosaran5504]

did you know you can calculate the circumference of a moose with quadruple integrals

[@gerald_the_science_guy]

PLS BE CAREFUL!!!! when u use u-subst., u have have pay attention to ur limits of int. because they will change...now it doesn't really matter in most cases because u know u'll eventually change back to ur original variables, but in an exam or in the case where u go ahead and work with 'u's, it could be very problematic. Just my two cents :)

[@hossamelalfy2387]

the same answer ,bro .she made a fault in u subst so the result is wrong

[@liquidnice4999]

Honestly i should be paying tuition to you not to my professors

[@draznitelka]

why didnt you have z=+/- sqrt of ... and you only had z=+sqrt 1+x2+y2? :)

[@SantiAprende]

i know this has nothing to do with calculus but you are the sexiest tutor i´ve ever seen.....just keep doing what you are doing

[@mrpeanutbutter6094]

Why can’t I find a girlfriend like you.

[@jamesmoriaty1098]

I'm gonna unsubscribe krista bcuz the calc level ur reviewing is too hard for me ! Jk with love