# Math Help - Triple Integral Problem

1. ## Triple Integral Problem

So I'm having a little trouble with a triple integral problem. I haven't done many of these, so I'm not sure if my bounds of integration are correct etc. Anyway, here is the problem as stated:

"f(x,y,z) = z

W is the region bounded by z=0, x^2 +4y^2=4 and z=x+2

Integrate f over the region W."

I've attached my attempt at solving this. Basically I'm stuck at evaluating the last iterated integral, which makes me think I've done something wrong before getting there...

Would appreciate any help!

2. ## Re: Triple Integral Problem

Originally Posted by gralla55
"f(x,y,z) = z W is the region bounded by z=0, x^2 +4y^2=4 and z=x+2 Integrate f over the region W."
Hint Using the transformation $(x,y,z)=(x,2v,z)$ and cylindric coordinates you'll obtain the region

$\begin{Bmatrix}0\leq \theta \leq 2\pi \\0\leq \rho \leq 2\\0\leq z \leq 2+\rho \cos\theta\end{matrix}$