∫π20cos2xcosx+sinxdx=______.-数学

题目简介

∫π20cos2xcosx+sinxdx=______.-数学

题目详情

π
2
0
cos2x
cosx+sinx
dx
=______.
题型:填空题难度:中档来源:沈阳二模

答案

定积分
class="stub"π
2
0
class="stub"cos2x
cosx+sinx
dx

=
class="stub"π
2
0
cos2x-sin2x
cosx+sinx
dx

=
class="stub"π
2
0
(cosx-sinx)dx

=(sinx+cosx)|0 class="stub"π
2
=1-1=0.
故答案为:0.

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