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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

$$\int_{-a}^{a}\int_{-\sqrt{a^2-x^2}}^{\sqrt{a^2-x^2}}\,dy\,dx$$

into an integral in polar coordinates and then evaluate it.

Changing to polar coordinates I got the integral

$$\int_{0}^{\pi}\int_{-a}^{a}r\,dr\,d\theta$$

and evaluating this integral I ended up with an integrand of 0 to integrate with respect to \(d\theta\) and I wasn't entirely sure how to integrate that so I thought it might just be \(\pi\).

I really feel like there's no way that answer could be correct, seeing as the integral is of half a circle with radius \(a\) and the answer has nothing to do with \(a\). If someone could let me know where I went wrong that would be great.