求定积分∫10(xex2+x2e2)dx.-数学

题目简介

求定积分∫10(xex2+x2e2)dx.-数学

题目详情

求定积分∫10(xex2+x2e2)dx.
题型:解答题难度:中档来源:福建

答案

10
(xex2+x2e2)dx=
10
xex2dx+
10
x2e2dx.

其中
10
xex2dx=class="stub"1
2
10
ex2dx2=class="stub"1
2
ex2
.
1
0
=class="stub"1
2
(e-1)


∫01(x2e2)dx=e2∫01x2dx=e2×
[
x3
3
]
10
=
e2
3

∴∫10(xex2+x2e2)dx=-∫01(xex2+x2e2)dx=-[class="stub"1
2
(e-1)+
e2
3
]=-
e2
3
-class="stub"1
2
e+class="stub"1
2

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