∫∫z^2ds,其中∑是上半球面z=√1-x^2-y^2被平面z=1/2截取的顶部
问题描述:
∫∫z^2ds,其中∑是上半球面z=√1-x^2-y^2被平面z=1/2截取的顶部
答
∫∫(1-x^2-y^2)√(1/(1-x^2-y^2)dxdy
=-1/2∫dθ∫√(1-r^2)dr^2
=7/(12π)是7π/12