# Double Integral with Polar Coordinates

#### Em Yeu Anh

$$\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx$$
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.

#### slovakiamaths

$$\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx$$
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.
put x=rcost and y=rsint, dxdy=rdrdt the solve it

#### 11rdc11

$$\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx$$
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.

$$\displaystyle y = \sqrt{2x - x^2}$$

$$\displaystyle y^2 = 2x -x^2$$

$$\displaystyle y^2 + x^2 = 2x$$

$$\displaystyle r^2 = 2r\cos{\theta}$$

$$\displaystyle r = 2\cos{\theta}$$

$$\displaystyle \int^{\frac{\pi}{2}}_{0} \int^{2\cos{\theta}}_{0} (5r)r drd\theta$$