用极坐标计算二次积分：∫(0,2)dx∫(0,x)f[(x^2+y^2)^(1/2)]dy

Question

如题所述

Answer 1

∫(0,2)dx∫(0,x)f[(x^2+y^2)^(1/2)]dy
=∫(0,Pi/4)dt∫(0,2/cost)f(r)rdr
因为 x=2 => r*cost = 2,
即 r = 2/cost