Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2 + y^2 = 100 and x^2 - 10x +y^2 = 0
If we convert the second circle to polar we have
$\displaystyle x^{2}+y^{2}-10x=0$
$\displaystyle r^{2}-10rcos{\theta}=0$
$\displaystyle r=10cos{\theta}$
The equation of the first circle is $\displaystyle r=10$
The area between them is:
$\displaystyle \frac{1}{2}\int_{0}^{\frac{\pi}{2}}[10^{2}-(10cos{\theta})^{2}]d{\theta}$