2. 考研
  3. 设f(x)连续，且g(x)＝∫0xx2f(x－t)dt，求g’(x)．

设f(x)连续，且g(x)＝∫0xx2f(x－t)dt，求g’(x)．

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问题 设f(x)连续，且g(x)＝∫0xx2f(x－t)dt，求g’(x)．
选项
答案g(x)＝－x2∫0xf(x－t)d(x－t)＝－x2∫x0f(u)du＝x2∫0xf(u)du， g’(x)＝2x∫0xf(u)du＋x2f(x)．
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考研数学三

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