z的积分上下限都是常数,其实就是化成极坐标求二重积分平面区域D,x^2+y^2<=2x得到r^2<=2rcosθ,即r<=2cosθy>=0得到rsinθ>=0,即0<=θ<=π注意D只在一四象限,0<=θ<=π/2原积分=∫(0,a)zdz∫(0,π/2)dθ∫(0,2cosθ)r^2dr=a^2/6∫(0,π/2)8(cosθ)^3dθ=2a^2/3∫cosθ(cos2θ+1)dθ=a^2∫cosθdθ+a^2/3∫cos3θdθ=a^2-a^2/9=8a^2/9