设连续函数f(x)满足∫0xtf(x—t)dt=1—cosx,求

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问题 设连续函数f(x)满足∫0xtf(x—t)dt=1—cosx,求

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答案由∫0xtf(x一t)dt[*]x∫0xf(u)du一∫0xuf(u)du得 x∫0xf(u)du一∫0xuf(u)du=1一cosx.两边求导得∫0xf(u)du=sinx,故[*]

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