用二重积分计算抛物面x2+y2=z和平面z=1所围的体积

是一个高为1的碗形旋转抛物面,底圆半径为1,
转换成极坐标,V=4∫[0,π/2]dθ∫[0,1][（rcosθ)^2+(rsinθ)^2]rdr
=4∫[0,π/2]dθ∫[0,1]r^3dr
=4∫[0,π/2] (r^4/4)[0,1]dθ
=[∫[0,π/2]dθ
=π/2.