# Triple Integral: Having trouble finding my y bounds

1. Nov 2, 2008

1. The problem statement, all variables and given/known data

$$I=\int\int\int_E x^2e^ydV$$ 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? :)

2. Nov 2, 2008

### Avodyne

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

3. Nov 3, 2008

### HallsofIvy

Staff Emeritus
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.

4. Nov 4, 2008