1. Prove that ∫(x=0 to π) xf(sinx) dx= π/2 ∫(x=0 to π) f(sinx) dx.
2. Given that ∫(x=0 to a) f(x)g(x) dx=K/2 ∫(x=0 to a)f(x) dx,f(x)=f(a-x) and g(x)+g(a-x)=K,where K is a constant.
Hence,or otherwise, evaluate ∫(x=0 to π) xsin^2xcos^4x dx
收錄日期: 2021-04-26 14:55:10
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