∫01dy∫1y/2cosx2dx+∫12dy∫y/21cosx2dx=________.

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问题01dy∫1y/2cosx2dx+∫12dy∫y/21cosx2dx=________.

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答案sin1/2

解析 改变积分次序得
01dy∫y/2ycosx2dx+∫12dy∫y/21cosx2dx=∫01dx∫x2xcosx2d(x2)=(1/2)sinx2|01
=sin1/2.
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