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The questions is to find the area in the bounded region in polar coordinates

$r = \sqrt{\theta}$ from $3\pi/2$ to $2\pi$

Here is what I did: I got the integral of $\cfrac{1}{2}\theta d\theta$ from $3\pi/2$ to $2\pi$. Then I integrated and got $\cfrac {1}{4} \theta ^2$ from $3\pi/2$ to $2\pi$. As a result, I got $\cfrac {7}{16}\pi^2$

But I felt that there might be something wrong with my answer. Can someone tell me about this? Thanks

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to find the area of the region in polar coordinates – Jaden Q Oct 21 '12 at 9:00
up vote 0 down vote accepted

The area is $\cfrac12\displaystyle\int_{{3\pi}/2}^{2\pi} [r(\theta)]^2 d\theta = \cfrac12\displaystyle\int_{{3\pi}/2}^{2\pi} \theta d\theta$ and this should return $\cfrac{7}{8}\pi^2$. Check your work again.

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