(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using cylindrical coordinates, evaluate ʃʃʃe^z where E is enclosed by the paraboloid z = 1 + x^2 + y^2 and the cylinder x^2 + y^2 = 5 and the xy-plane.

2. Relevant equations

3. The attempt at a solution

here are the integrals in xyz coordinates:

0>z>1 + x^2 + y^2

-(5-x^2)^.5 > y > (5 - x^2)^.5

-(5)^.5 > x > (5)^.5

i double checked that with my proffessor so it has to be right. but i must be doin something wrong when i switch into polar coordinates. here is what the polar limits are (i thought):

0 > z > 1 + r^2

0 > r > 5^.5

0 > ɵ > 2pi

i keep getting the wrong answer. if anything is wrong i would think it is z. unless maybe it is right and i am just integrating wrong but i checked over a million times and didnt c any mistakes :( i have:

ʃʃʃ(e^z)rdzdrdɵ

edit: let me know if u need more info. i can type out all my integration steps if u think my limits look good

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# Homework Help: Tripple integral

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