Question

Evaluate the triple integral ∭Ex^2e^ydV where E is bounded by the parabolic cylinder z=9−y^2 and the planes z=0,x=3, and x=−3.

little confused on what my bounds are supposed to be.....help?

Answer 1

i think x is gonna be -3,3, z is 0 to 9-y^2, but not sure on y.

Answer 2

\[\int\limits\limits_{-3}^{3}\int\limits\limits_{-\sqrt(9-z)}^{\sqrt(9-z)}\int\limits\limits_{0}^{9-y^2}x^2e^ydzdydx\]

Answer 3

try
\[\int\limits\limits_{-3}^{3}~~\int\limits\limits_{-3}^{3}~~\int\limits\limits_{0}^{9-y^2}x^2e^ydzdydx\]

Answer 4

yes, that's correct. ok, why are my y bounds not equations? i drew it out in an online grapher and the y was bounded by the parabola....or was i looking at it wrong?

Answer 5

lets see the picture in yz plane