Converting triple integrals to cylindrical coordinates (KristaKingMath)

Learn how to convert a triple integral from cartesian coordinates to cylindrical coordinates. You'll need to convert the function itself, the order of integration, and the limits of integration before evaluating the triple integral in cylindrical coordinates.

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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?!”

[kristakingmath]

Hi all! At 5:56 the bounds for r should be [0, 2] instead of [-2, 2]. I have an annotation for this, but sometimes annotations don't show up depending on your settings and where you're watching.

[ThePhillyg]

13 minutes of work for the answer of ZERO. Ladies and Gentlemen... Calculus.

[paclax]

amazing explanation and video, however the bounds for r should be 0<r<2. -2<r<2 gives diameter where r needs to be in terms of the radius

[DreamscaperTV]

OMG! You have opened my eyes, this is easier than I expected.

[cloudsmasher]

this is amazing. i have been trying to learn this for hours, and now it all makes sense

[harishbaskar]

guys small mistake. r is from 0 to 2...
x=[0, 2] its the radius not diameter

[kristalenee]

This really helped me but why did you make r from (-2, 2) instead of from (0, 2) ?

[jenniferf]

Perfectly taught! You make Calculus simple and understandable. Much better job than most professors. Thanks so much!

[thabangmthethwa]

...am a second year student studying Civil engineering. i don't go to lectures anymore. the videos u make are even better than going to lectures. you are a good teacher. thank you very much.

[favio]

yo math lady u ma nigga, save the day...erryday...

[dstan]

Thank you Ma'am...This video really helped a lot...👍👍👍

[SkatingToy]

Thanks for the explanation. The only thing I'm confused about is theta's limits. When is it not from 0 to 2pi? Is it different if there are variables for the y limits? Great tutorial nonetheless, much better than my professor haha

[ungell]

Elegant explanation- keep up the good work! Thank you, I appreciate your videos!

[sirangus]

This was almost an exact problem my prof went over in class...only you explained it so much better. Thanks CE!! You''re the bomb!!!

[LeonTGBU]

When converting to polar you have to set your r value to absolute value after conversion otherwise you will obtain a double of the actual volume.

[mohannedalghazo]

Thank you for pinning the correction because it was going to make me so confused!. Anyhow, it was a great explanation and thank you so much!!

[JKhal]

Amazing vid!
from the step where you get cos(theta) x [16/3 - 32/10 ],
simplified to 32/15 x cos(theta)

[rodyys]

you're the best! This video is what i was looking for like 40 minutes!

[vor]

damn you are even explaining common denominator in triple integrals in cylindrical coords video
thats why you are great teacher, i passed calculus with high marks thanks to you (and pauls notes website)

[AnonymousIdiott]

Hey Krista, why is the range for theta 0 to 2pi? Why is it not 0 to pi due to the fact the circle goes from 2 to -2?