计算积分I=∫(0,2a)dx∫[0,(2ax-x^2)^1/2](x^2+y^2）dy.

换到极坐标系,积分区域D：0≤ θ ≤ π/2,0≤ p ≤ 2a cosθ
I = ∫[0,π/2] dθ ∫ [0,2a cosθ] p^3 dp
= ∫[0,π/2] 4 a^4 (cosθ)^4 dθ
= 4 a^4 * (3π/16)
= 3π a^4 /4