把下列积分化为极坐标形式,并计算积分值 ∫（上限是1,下限是0）dx∫(上是√x-x^2,下是0)(x^2+y^2)dy

原式=∫dθ∫r²*rdr
=∫[(r^4/4)│]dθ
=∫[(cosθ)^4/4]dθ
=∫[3/24+cos(2θ)/8+cos(4θ)/32]dθ
=[3θ/24+sin(2θ)/16+sin(4θ)/128]│
=(3/24)(π/2)+0+0
=3π/48