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Question

The value of 012af(x)f(x)+f(12a-x)dx is


A

a

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B

2a

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C

3a

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D

6a

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Solution

The correct option is D

6a


Explanation for the correct answer.

Evaluate the integral.

I=012af(x)f(x)+f(12a-x)dxI=012af(12a-x)f(12a-x)+f(x)dx2I=012af(x)+f(12a-x)f(12a-x)+f(x)dx2I=012adx=x012a=(12a-0)=12aI=6a

Hence, option D is correct .


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