JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int_0^{\infty} f(x) d x=\frac{\pi}{2}

and

f(x)

is an even function, then

\int_0^{\infty} f\left(x-\frac{1}{x}\right) d x

is equal to

View answer and explanation

Correct option: B

\frac{\pi}{2}

Option B (

\frac{\pi}{2}

) is correct because the integral of

f(x-\frac{1}{x})

from 0 to infinity is equal to the integral of

f(x)

from 0 to infinity when

f(x)

is an even function.

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