填空题
13.∫02dx∫x2y2e-y2dy=_______．
- 1、
【正确答案】
1、
【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-t｜04+
∫04e-tdt
=-2e-4-
e-t｜04=
e-4+
∫02dx∫x2y2e-y2dy=∫02dy∫0yy2e-y2dx=∫02y3e-y2dy=
∫02y2e-y2d(y2)=∫0tte-tdt=
∫04td(e-t)=te-t｜04+∫04e-tdt=-2e-4-
e-t｜04=e-4+