Let D= {(x, y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?

In polar coordinates, the inequality changes to

which is a circle of radius 2 and centered at (2, 0). The set D is then

The integral is then

There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,

so that the integral is

Then invoke another double-angle formula,

to change the integral to

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step-by-step explanation: