Solving integral containing unknown values

Question:Solving integral containing unknown values

Posted: Calor1 15

April 11 2014

Is there a way to solve the following integral completely?

int(int(x^2+y^2, y = -sqrt(2*a*x-x^2) .. sqrt(2*a*x-x^2)), x = 0 .. 2*a)

When I try solving that all I get is the following:

$\int_{0}^{2a}(2x^2)\sqrt{2ax-x^2}+\frac{2}{3}(2ax-x^2)^\frac{3}{2}dx$

All is well when I calculate it using polar coordinates though:

int(int(r^3, r = 0 .. 2*a*cos(t)), t = -(1/2)*Pi .. (1/2)*Pi)

= $\frac{3}{2}a^4\pi$

Why doesn't maple solve the first one completely and is there a way around this?

Thanks

Calor

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