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Question

f(x) is a continuous functions for all real values of x and satisfies n+1nf(x)dx=n22,nϵZ, then 53f(x)dx is equal to

A
92
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B
72
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C
352
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D
None of these
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Solution

The correct option is A 92
We have, I=53f(|x|)dx

I can also be written as

I=23f(|x|)dx+12f(|x|)dx+01f(|x|)dx+10f(x)dx+21f(x)dx+32f(x)dx+43f(x)dx+54f(x)dx

I=210f(x)dx+221f(x)dx+232f(x)dx+43f(x)dx+54f(x)dx

I=02+22+82+92+162=13+92=352

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