# Thread: Setting up triple integral

1. ## Setting up triple integral

Edit: Title should read double integral... oops

Having a little trouble figuring this one out.

Region bounded by 4x^2 + y^2 = 4z and z = 2

Thanks.

2. The two surfaces intersect when

$4x^2+y^2=4\cdot 2=8.$

What shape does this define? Would it be easier to use Cartesian or polar coordinates?

3. I was assuming that I should use polar coordinates, but I'm still not quite sure how to set it up.

4. The equation that bounds the region of integration can be rewritten

$\left(\frac{x}{\sqrt{2}}\right)^2+\left(\frac{y}{2 \sqrt{2}}\right)^2=1.$

This defines an ellipse whose equation in polar coordinates is

$r=\sqrt{2}\cos\theta + 2\sqrt{2}\sin\theta.$