# Math Help - help me with triple integral

1. ## help me with triple integral

$\int \int_{E} \int x^2e^y dV$

E is bounded by parabolic cylinder $z = 1-y^2$ and the plane z=0, x=1 and x=-1
so the boundary should be:

$0 \leq z \leq 1-y^2$

$-1 \leq y \leq 1$

$-1 \leq x \leq 1$

are they right?

2. Looks good.

3. but if i integrate this: $\int^1_{-1} \int^1_{-1} \int^{1-y^2}_0 x^2e^y dz dy dx$, I got zero eventually which is not possible.

What is wrong?

4. Originally Posted by zpwnchen
but if i integrate this: $\int^1_{-1} \int^1_{-1} \int^{1-y^2}_0 x^2e^y\,dz\,dy\,dx$, I got zero eventually which is not possible.

What is wrong?
I just evaluated it on my TI-89 and got

$-\frac{2(e^2-5)}{3e}$