Question

证明广义积分：积分号0到π/2 sin(secx)dx 绝对收敛

Answer 1

令 secx=t cosx=1/t x=arccos1/t

dx={-1/√[1-(1/t)^2]}(-1/t^2)dt=1/[t√(t^2-1)]dt

x=0 时 t=1 x=π/2时 t=+