2. 考研
  3. ∫02dy∫y2x2ex2dx=_________．

∫02dy∫y2x2ex2dx=_________．

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问题 ∫02dy∫y2x2ex2dx=_________．
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答案[*]
解析 改变积分次序得
∫02dy∫y2x2ex2dx=∫02x2ex2dx∫0xdy=∫02x3ex2dx
=∫02x2ex2d(x3)∫04tetdt
=(t-1)et｜=
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考研数学三

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