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## Homework Statement

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x

^{2}+ y

^{2}= 256 and x

^{2}- 16x + y

^{2}= 0.

## Homework Equations

## The Attempt at a Solution

Finding the intervals of integration for the polar coordinates.

From the first equation I get r

^{2}= 256 therefore r = 16

From the second equation I get r

^{2}- 16rcos[tex]\theta[/tex] therefore r = 16cos([tex]\theta[/tex])

Since it is the first quadrant theta will be from 0 to pi/2.

Now this is the part where I am confused about. My intuition is that I should integrate the bigger circle and then subtract the integral of the smaller circle within it so I would have something like the following.

[tex]\int^{\pi/2}_{0}\int^{16}_{0} r drd\theta - \int^{\pi/2}_{0}\int^{16cos\theta}_{8} r drd\theta[/tex].

Is this the right approach?