Find the area of the region by double integration

**ElTaco** · March 30th 2011, 02:43 PM

The question states:

Find the area of the region by double integration.

The region inside the circle $r=4cos(\Theta)$ but outside the circle $r=2$ .

I set up the problem with $\int_{0}^{2\pi} \int_{2}^{4cos\Theta} rdrd\Theta$

However, the answer I got in the end was $4\pi$ , I'm assuming it's because of the way I set it up rather than a calculation error since I did it several times. The correct answer according to the textbook is $4\pi/3 +2\sqrt{3}$ .

Thanks, any help would be appreciated.

**ojones** · March 30th 2011, 05:01 PM

You're $\theta$ limits are incorrect.

**ElTaco** · March 31st 2011, 06:06 AM

Thank you very much, I figured out what the actual theta parameters are.

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