计算下列定积分的值(1)∫π20(x+sinx)dx(2)∫31(x+1x)26xdx(3)∫321-xx2dx(4)∫π2-π2cos2xdx.-数学

题目简介

计算下列定积分的值(1)∫π20(x+sinx)dx(2)∫31(x+1x)26xdx(3)∫321-xx2dx(4)∫π2-π2cos2xdx.-数学

题目详情

计算下列定积分的值
(1)
π
2
0
(x+sinx)dx
 
(2)
31
(
x
+
1
x
)
2
6xdx

(3)
32
1-x
x2
dx

(4)
π
2
-
π
2
cos2xdx
题型:解答题难度:中档来源:不详

答案

(1)
class="stub"π
2
0
(x+sinx)dx
=(class="stub"1
2
x2-cosx)|0 class="stub"π
2
=1+
π2
8

(2)
31
(
x
+class="stub"1
x
)
2
6xdx
=
31
(6x2+12x+6)dx=(2x3+6x2+6x)
|31
=112;
(3)
32
class="stub"1-x
x2
dx
=(-class="stub"1
x
-lnx)
|32
=ln2-ln3+class="stub"1
5

(4)
class="stub"π
2
-class="stub"π
2
cos2xdx
=
class="stub"π
2
-class="stub"π
2
class="stub"cos2x+1
2
dx
=class="stub"1
2
class="stub"1
2
sin2x
+x)
|class="stub"π
2
-class="stub"π
2
=class="stub"π
2

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