设et2dt=∫0xcos(x-t)2dt确定y为x的函数,求.

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问题et2dt=∫0xcos(x-t)2dt确定y为x的函数,求

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答案0xcos(x-t)2dt[*]∫x0cosu2(-du)=∫0xcost2dt, 等式∫1y-x2et2dt=∫0xcost2两边对x求导,得[*]=cosx2, 于是[*]cosx2

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