Evaluate the double integral by converting to polar coordinates

[alanthreonus]

Homework Statement

Convert to polar coordinates to evaluate

$$\int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydx$$

The Attempt at a Solution

Really I'm just not sure how to convert the limits of integration. I know $$\sqrt(2x-x^2)$$ is a half-circle with radius 1, but I'm not really sure where to go from there.

 

[rock.freak667]

By √(2x-x) do you mean just √x ?

 

[ideasrule]

A half-circle with radius 1 would be y=sqrt(1-x^2), not what you wrote.

 

[alanthreonus]

Woops, I meant sqrt(2x-x^2)