GATE 2015 CS – Question 58
$\int_{1/\pi}^{2/\pi} \frac{\cos(1/x)}{x^2} \, dx =$ ________.
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Correct answer: -1
Explanation
Substitute $u = \frac{1}{x}$, so $du = -\frac{dx}{x^2}$. The limits $x = \frac{1}{\pi}$ and $x = \frac{2}{\pi}$ become $u = \pi$ and $u = \frac{\pi}{2}$. The integral is $-\int_{\pi}^{\pi/2} \cos u \, du = \int_{\pi/2}^{\pi} \cos u \, du = \sin \pi - \sin \frac{\pi}{2} = -1$.