2. 考研
  3. 设f’(x)=arcsin(x一1)2，f(0)=0，求∫01f(x)dx．

设f’(x)=arcsin(x一1)2，f(0)=0，求∫01f(x)dx．

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问题 设f’(x)=arcsin(x一1)2，f(0)=0，求∫01f(x)dx．
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答案∫01f(x)dx=∫01f(x一1)=(x—1)f(x)｜01一∫01(x一1)f’(x)dx =f(0)一∫01(x一1)f’(x)dx=一∫01(x一1)arcsin(x一1)∫01dx [*]
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