设f(x)∈C[0,1],证明∫（π,0）*x*f(sinx)dx =π/2*∫（π,0）*f(sinx)dx
人气：183 ℃ 时间：2019-10-03 08:45:48
解答
设x = π - y,dx = - dy当x = 0,y = π当x = π,y = 0∫(0→π) xf(sinx) dx = - ∫(π→0) (π - y)f(sin(π - y)) dy= π∫(0→π) f(siny) dy - ∫(0→π) yf(siny) dy= π∫(0→π) f(sinx) dx - ∫(0→π) xf(s...
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