把下面这积分化为极坐标形式下的二次积分

积分区域是半圆,化成极坐标为：r=2acosθ,(0≤θ≤π）
原式=∫[0,π/2]dθ ∫[0,2acosθ ] (r^2*r)dr
=∫[0,π/2]dθ [0,2acosθ [ r^4/4
=(1/4)∫[0,π/2]dθ [0,2acosθ ] (cosθ )^4
=(16a^4/4)∫[0,π/2]dθ [1+cos2θ)^2/4
=a^4∫[0,π/2]dθ [1+2cos2θ+(cos2θ)^2]
=a^4[θ+sin2θ+θ/2+(sin4θ)/8][0,π/2]
=a^4(3/2*π/2+0+0）
=3πa^4/4.