设f(x)为连续函数,证明: ∫02πf(|sinx|)dx=4∫0π/2f(sinx)dx.

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问题 设f(x)为连续函数,证明:
0f(|sinx|)dx=4∫0π/2f(sinx)dx.

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答案0f(|sinx|)dx=∫πf(|sinx|)dx=2∫0πf(|sinx|)dx=2∫0πf(sinx)dx=4∫0π/2f(sinx)dx.

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