填空题
7.∫02dy∫y2x2ex2dx=_________．
- 1、
【正确答案】
1、
【答案解析】改变积分次序得
∫02dy∫y2x2ex2dx=∫02x2ex2dx∫0xdy=∫02x3ex2dx
=
∫02x2ex2d(x3)
∫04tetdt
=
(t-1)et｜=
∫02dy∫y2x2ex2dx=∫02x2ex2dx∫0xdy=∫02x3ex2dx
=
∫02x2ex2d(x3)∫04tetdt=
(t-1)et｜=