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

设f(x)连续，则d2/dx2∫0xtf(x-t)dt=________．

admin2021-10-18  45
问题 设f(x)连续，则d2/dx2∫0xtf(x-t)dt=________．
选项
答案f(x)
解析 由∫0xtf(x-t)dt→∫x0(x-u)f(u)(-du)=x∫0xf(u)du-∫0xuf(u)du得d/dx∫0xtf(x-t)dt=d/dx[x∫0xf(u)du-∫0xuf(u)du]=∫0xf(u)du+xf(x)-xf(x)=∫0xf(u)du，故d2/dx2∫0xtf(x-t)dt=d/dx∫0xf(u)du=f(x)．
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考研数学二

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