Double Integral with Polar Coordinates

Nov 2009
94
6
\(\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx \)
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.
 
Apr 2010
41
15
India
\(\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx \)
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
 
Jul 2007
894
298
New Orleans
\(\displaystyle \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx \)
Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.

\(\displaystyle y = \sqrt{2x - x^2}\)

\(\displaystyle y^2 = 2x -x^2\)

\(\displaystyle y^2 + x^2 = 2x\)

\(\displaystyle r^2 = 2r\cos{\theta}\)

\(\displaystyle r = 2\cos{\theta}\)

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