若(x2-1ax)9的展开式中x9的系数为-212,则∫a0sinxdx的值等于()A.1-cos2B.2-cos1C.cos2-1D.1+cos2-高二数学

题目简介

若(x2-1ax)9的展开式中x9的系数为-212,则∫a0sinxdx的值等于()A.1-cos2B.2-cos1C.cos2-1D.1+cos2-高二数学

题目详情

若(x2-
1
ax
9的展开式中x9的系数为-
21
2
,则
a0
sinxdx的值等于(  )
A.1-cos2B.2-cos1C.cos2-1D.1+cos2
题型:单选题难度:中档来源:不详

答案

Tr+1=
Cr9
(x2)9-r(-class="stub"1
ax
)r
=(-class="stub"1
a
)r
Cr9
x18-3r

取18-3r=9,得r=3.
(-class="stub"1
a
)3
C39
=-class="stub"21
2
,解得:a=2.
a0
sinxdx=
20
sinxdx=-cos
x|20
=1-cos2.
故选:A.

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