# $\int_{0}^{6} \int_{0}^{y} x dx dy$ 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
In the future, please try to ask questions instead of merely stating the problem, and also try to use proper LaTeX formatting. I cleaned this post up, but it would be helpful if in the future you do that yourself. Also, if this is a homework problem please add the "homework" tag. Lastly, can you tell us how you've tried to evaluate this and where you've gotten stuck? –  Alex Becker Apr 27 '11 at 5:24
@Alex: Others may disagree, but I would say this is too much help to give OP in asking a coherent question. Your section on "what have you tried" is very well posed (we don't know if it is well taken). –  Ross Millikan Apr 27 '11 at 5:26
@Ross: I figured I should give the OP a break as I thought this was his/her first post, but I just realized that this is a duplicate of one asked less than an hour ago. I certainly wouldn't do this for someone I who'd used the site before. –  Alex Becker Apr 27 '11 at 5:28
@Alex: fair enough. We all have different thresholds. I'm the +1 on your comment. –  Ross Millikan Apr 27 '11 at 5:31

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.