Question

求解高等数学题，如图，请给出计算过程

Answer 1

let

x=π+u

du = dx

x=π, u=0

x=2π , u=π

∫(π->2π) (sinx)^n . (cosx)^m dx

=∫(0->π) (-sinu)^n . (-cosu)^m  du

=-∫(0->π) (sinu)^n . (cosu)^m  du

=-∫(0->π) (sinx)^n . (cosx)^m  dx

∫(0->2π) (sinx)^n . (cosx)^m dx

=∫(0->π) (sinx)^n . (cosx)^m dx +∫(π->2π) (sinx)^n . (cosx)^m dx

=∫(0->π) (sinx)^n . (cosx)^m dx  -∫(0->π) (sinx)^n . (cosx)^m dx 

=0

Answer 2

0