# $\int_{0}^{6} \int_{0}^{y} x dx dy$ where $x = r \cos \theta, y = r \sin \theta, dx dy = r dr d \theta$

Given $x = r \cos \theta, y = r \sin \theta, dx dy = r dr d \theta$, how can I evaluate the following integral: $\int_{0}^{6} \int_{0}^{y} x dx dy$

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I would calculate it in Cartesian coordinates (do you need to evaluate it in polar coordinates?) – Fabian Apr 27 '11 at 5:21

First, substitute everything in for $x\,dx\,dy$. Next find the limits of integration in terms of $r$ and $\theta$. Personally, I recommend drawing a picture of the region of integration.