GATE 2019 EC – Question 29
The value of the integral $\displaystyle\int_0^\pi\int_y^\pi\frac{\sin x}{x}\,dx\,dy$ is equal to ________.
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Correct answer: 2
Explanation
Swap the order of integration: the region is $0\le y\le x\le\pi$, so the integral is $\int_0^\pi\frac{\sin x}{x}\left(\int_0^xdy\right)dx=\int_0^\pi\sin x\,dx=2$.