设f(x)连续，则d2/dx2∫0x(x-t)f(t)dt=________．

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问题设f(x)连续，则d²/dx²∫₀^x(x-t)f(t)dt=________．

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答案f(x)

解析由∫₀^x(x-t)f(t)dt=x∫₀^xf(t)dt-∫₀^xtf(t)dt，则d/d∫₀^x(x-t)f(t)dt=∫₀^xtf(t)dt+xf(t)-xf(x)=∫₀^xtf(t)dt，于是d²/dx²∫(x-t)₀^xtf(t)dt=f(x)．

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考研数学二

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