原式=∫∫√(a²-x²)dzdx-∫∫[-√(a²-x²)]dzdx+∫∫(x+1)dxdy-∫∫(x+0)dxdy
(S1：-a≤x≤a:,0≤z≤1.S2：x²+y²≤a²)
=2∫∫√(a²-x²)dzdx+∫∫dxdy
=2∫√(a²-x²)dx∫dz+∫dθ∫rdr (第二個(gè)積分作極坐標(biāo)變換)
=2∫√(a²-x²)dx+πa²
=2∫a²cos²tdt+πa² (作變換x=asint)
=a²∫[1+cos(2t)]dt+πa² (應(yīng)用倍角公式)
=a²[t+sin(2t)/2]│+πa²
=a²(π/2+π/2)+πa²
=2πa².