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Question

The value of -ππcos2(x)1+axdx,a>0 is


A

2π

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B

πa

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C

π2

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D

aπ

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Solution

The correct option is C

π2


Explanation for the correct option:

Compute the required value:

Given: -ππcos2(x)1+axdx

Let I=-ππcos2(x)1+axdx-------(1)

substitute xπ+(-π)-x-x

I=-ππcos2(x)1+axdx-ππcos2(-x)1+a-xdxI=-ππcos2(x)1+1axdxI=-ππaxcos2(x)ax+1dx-----(2)

Add equations (1) and (2)

I+I=-ππcos2(x)1+axdx+-ππaxcos2(x)1+axdx2I=-ππ(1+ax)cos2(x)1+axdx2I=-ππcos2(x)dx2I=-ππ1+cos2x2dxI=14-ππ(1)·dx+-ππcos(2x)dxI=14x-ππ+sin(2x2-ππI=14π+π+sin(2π)+sin(2π)2I=π2

Hence, option A is the correct answer.


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