设f(2)=,f’(2)=0,∫02f(x)dx=1,求∫01x2f’’(2x)dx.

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问题 设f(2)=,f’(2)=0,∫02f(x)dx=1,求∫01x2f’’(2x)dx.

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答案01x2f’’(2x)dx=[*]∫01(2x)2f’’(2x)d(2x)[*]∫02t2f’’(t)dt =[*]∫02t2d[f’(t)]=[*][t2f’(t)|02-2∫02tf’(t)dt] =[*]∫02tdf(t)=[*][tf(t)|02-∫02f(t)dt] =[*][2f(2)-1]=0.

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