原式=∫dx∫√(y-x²)dy =(2/3)∫(1-x²)^(3/2)dx =(2/3)∫(cost)^4dt (令x=sint) =(2/3)∫[3/8+cos(2t)/2+cos(4t)/8]dt =(2/3)[3t/8+sin(2t)/4+cos(4t)/32]│ =(2/3)(3π/16+3π/16) =π/4.
