# Struggling with the integration part

1. Jan 22, 2008

### rolylane

Hi
I've been working on a problem and I'm nearly there but I'm struggling with the integration part at the end and was hoping you might be able to help if you have the time. The original question was

$$\int \int (y^2 z^2 + z^2 x^2 + x^2 y^2) \: dS$$
Evaluated on the region of $$z^2 = x^2 + y^2$$ between z=1 and z=2.
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Then by substituting in x=r*cos(θ) and y=r*sin(θ), and multiplying by 'r' (the Jacobian determinant), I got $$\sqrt{2} \int_{0}^{2\pi} \int_{1}^{2}(r^5 + r^3 \cos(\theta)^2 \sin(\theta)^2) \: dr \: d\theta$$

and then I'm stuck. Any help or advice would really be appreciated
Thanks