∫02dx∫x2y2e-y2dy=_______.

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问题02dx∫x2y2e-y2dy=_______.

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答案[*]

解析 改变积分次序得
02dx∫x2y2e-y2dy=∫02dy∫0yy2e-y2dx=∫02y3e-y2dy=02y2e-y2d(y2)=0tte-tdt
=04td(e-t)=te-t04+04e-tdt
=-2e-4-e-t04=e-4+
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