积分∫f(sinx)/[f(cosx)+f(sinx)]dx= 在0到π/2的范围内

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积分∫f(sinx)/[f(cosx)+f(sinx)]dx=在0到π/2的范围内积分∫f(sinx)/[f(cosx)+f(sinx)]dx=在0到π/2的范围内积分∫f(sinx)/[f(cosx

积分∫f(sinx)/[f(cosx)+f(sinx)]dx= 在0到π/2的范围内
积分∫f(sinx)/[f(cosx)+f(sinx)]dx= 在0到π/2的范围内

积分∫f(sinx)/[f(cosx)+f(sinx)]dx= 在0到π/2的范围内

I=∫(0->π/2){ f(sinx)/[f(cosx)+f(sinx)] }dx
let
y =π/2-y
dx= -dy
x=0 ,y=π/2
x=π/2, y=0
I=∫(0->π/2){ f(sinx)/[f(cosx)+f(sinx)] }dx
=∫(π/2->0){ f(cosy)/[f(siny)+f(cosy)] }(-dy)
=∫(0->π/2){ f(cosy)/[f(siny)+f(cosy)] }dy
2I =∫(0->π/2) dx
= π/2
I = π/4