Finding the area enclosed by 4 functions using polar coordinates

Question

I need to find the area enclosed by $x^2+y^2$ = 4x, $x^2+y^2$ = 2x, y=x and y=0.

How do I use polar coordinates here? It seems to me that representing those functions using polar coordinates is too complex. Any help will be appreciated.

Answer 1

Unfortunately, this problem is ambiguous, but let's assume they want the area between the two circles:

Since $x^2+y^2=4x\implies r^2=4r\cos\theta\implies r=4\cos\theta$

and $\;\;x^2+y^2=2x\implies r^2=2r\cos\theta\implies r=2\cos\theta$,

$\;\;\;A=\displaystyle\int_0^{\frac{\pi}{4}}\int_{2\cos\theta}^{4\cos\theta} r\;dr d\theta$.