Question

f为连续函数 证明f(cosx)dx=f(sinx)dx 左右边的范围都是0到π /2

Answer 1

I = ∫[0,π/2] f(cosx) dx 换元,令 u= π/2-x,dx = (﹣1)du

= ∫[π/2,0] f(sinu) (-1)du

= ∫[0,π/2] f(sinu) du

= ∫[0,π/2] f(sinx) dx