# Double Integral with Polar Coordinates

• May 25th 2010, 09:19 PM
Em Yeu Anh
Double Integral with Polar Coordinates
$\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx$
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.
• May 25th 2010, 09:34 PM
slovakiamaths
Quote:

Originally Posted by 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.

put x=rcost and y=rsint, dxdy=rdrdt the solve it
• May 25th 2010, 10:02 PM
11rdc11
Quote:

Originally Posted by 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.

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

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

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

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

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

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