设f(x)在[a,b]上有连续的导数,f(a)=f(b)=0,且f2(x)dx=1,试求xf(x)f'(x)dx.

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问题 设f(x)在[a,b]上有连续的导数,f(a)=f(b)=0,且f2(x)dx=1,试求xf(x)f'(x)dx.

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答案[*]xf(x)fl(x)dx=[*]xf(x)d[f(x)]=[*]xd[f2(x)] =[*]

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