If and is an even function

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

If ∫0∞f(x)dx=π2\int_{0}^{\infty} f(x) dx = \frac{\pi}{2} and f(x)f(x) is an even function, then ∫0∞f(x−1x)dx\int_{0}^{\infty} f\left(x - \frac{1}{x}\right) dx is equal to (1) π4\frac{\pi}{4} (2) π2\frac{\pi}{2} (3) π\pi (4) None of these

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