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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