Calculus 3 Final Review (Part 2) || Double Integrals, Triple Integrals, Change of Variables

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Have you ever wondered what double and triple integrals actually tell you? Well have no fear because I'm about to teach all that to ya. We're gonna go over loads of practice problems with double and triple integrals, and we're also going to do the widely loved change of variables method for a multiple integral problem. Enjoy!

Timestamps:

00:01:30 - What do Double and Triple Integrals tell you?
00:08:40 - Double Integrals over Rectangles
00:16:40 - Double Integrals over General Regions
00:26:14 - Double Integrals using Polar Coordinates
00:39:45 - Triple Integrals
00:49:05 - Triple Integrals in Cylindrical Coordinates
00:59:20 - Triple Integrals in Spherical Coordinates
01:08:30 - Change of Variables in Multiple Integrals

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[LudusYT]

Donations really help me get by. If you'd like to donate, I have links below!!!
Venmo: @Ludus12
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Patreon: patreon.com/ludus1

[forceview]

Well I’m just here seeing what the future holds. Just passed Calc 2 with a 75

[masonreno]

Its crazy to me that you can learn every everything in calc 3 in 3 videos. for free.

[mingyuetang]

Hands down the best cal3 review video!!! I took multivariable calculus in cal with a super famous professor who has cal3 video on MIT opencourse, and you explain the material even better than him.

[litang]

I've been struggling a lot this semester (I haven't been putting in the work I should be), but your videos have been helping me SO SO much. You explain everything so well it's insane.

[jakeheckert]

Once again, your videos have helped me prepare for exams since they are comprehensive and put concepts in relation to the other skills students need to succeed in these calculus courses. And once again, I thank you for the time you put into creating these all while maintaining your own academic success. Thanks Josh!

[erich]

THANK BROOOO omg dude like im crying rn

[nikolaimikhail]

I'm so scared, this final has literally shown up in my nightmares

[liamsexton]

So incredibly helpful. Excellent explanations and examples. This is really gonna help me pass my test.

[tobeejefferson]

Ludas.. Man.. That trick with Jacobians.. You're a god. Why haven't I seen this? The system of equations is torture. Thank you.

[jas.x]

hi ludus, i found this video really helpful! just one quick note: i think the you need to take the abs value of the jacobian when you substitute it into the double integral, so it should've been positive 1/2.

[Dina-heuc]

i never understood the inverse of the jacobian thing, my textbook used like a whole page explaining it and it made no sense, yoou made it so simple thank u :)

[Armand__]

that jacobian trick was bomb. thx my guy

[bigdshlongmcdong]

God Bless you beautiful soul, you make your bloodline proud

[geromeabad]

Got a final today for calc 3 this helped a lot thanks bro!

[coletongross]

I think there's a mistake at 1:16:26, you put dy/dv instead of dv/dy. Same answer for the Jacobian but idk if that is a coincidence or not.

[doradorahaisai]

Thank you for showing that trick for calculating a Jacobian.

[mathewhanna]

hey @ludus so i understand how you are getting the limits @21:50 but is is okay for the lower limit to be x^2 and the upper to be rad x? For the first integral dy. I feel like that doesnt make sense, can u make a further explanation? Thank you

[michaelmalgioglio]

Isn’t the Jacobian supposed to be an absolute value?

[jasonrichards]

Thank you for your help. Hopefully I can ace this final!