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given the following region $R=\lbrace m,n \geq0$, $1 \geq m+n \geq 2\rbrace$ where $(m,n) \in \mathbb{R}^2$.write in polar coordinates $(r, \theta)$ the following double integral $\int\int_R m \,dA$

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my answer was $\int_{0}^{\frac{\pi}{2}}$ $\displaystyle\int_{\frac{1}{(cos \theta+ sin\theta)}^{\frac{2}{(cos \theta+ sin\theta)}}}$ $r^2$ cos $\theta$ dr d$\theta$. Is this answer true? –  nour Jun 10 '12 at 22:35
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Yes. You are correct. $\int_0^{\frac{\pi}{2}}\int_{\frac{1}{\cos\theta + \sin\theta}}^{\frac{2}{\cos\theta +\sin\theta}}r^2\cos\theta drd\theta$. –  M.B. Jun 10 '12 at 22:45
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