Triple Integral: Having trouble finding my y bounds

[Saladsamurai]

Homework Statement

$$I=\int\int\int_E x^2e^ydV$$ where E is bounded by the parabolic cylinder

z=1-y^2 and the planes z=0 x=1 and x=-1

I know that the graph is a parabola that opens downwards and that has symmetry wrt the x-axis. It also stretches along the x-axis toward + and - infinity.

Can I get a hint here? :)

 

[Avodyne]

Did you mean
$$I=\int\int\int_E x^2e^y\,dV$$ ?

 

[HallsofIvy]

It's pretty close to being trivial. The parabola z= 1- y² has z= 0 at y= -1 and y= 1 so projecting down on to xy=plane, we get the square -1< x< 1, -1< y< 1. The z- integral is taken from 0 to 1- y², the y integral from -1 to 1, and the x integral from -1 to 1.

 

[Saladsamurai]

Did you mean
$$I=\int\int\int_E x^2e^y\,dV$$ ?

I don't see any difference. So yes.