Question

计算球面x^2+y^2+z^2=4被柱面x^2+y^2=2y截下部分的面积？

Answer 1

2∫∫dS=2∫∫[2/(4-x^2-y^2)^(1/2)]dxdy

=2∫∫[2/(4-r^2)^(1/2)]rdrd(thta) r从0到1，thta从0到2pi

=8pi∫[1/(4-r^2)^(1/2)]dr 【换元法】

=8pi(2-根号3)