GATE 2026 AG – Question 36
Evaluate $I=\int_0^1\int_0^1x\cos(xy)\,dx\,dy$.
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Correct answer: (A) $1-\cos1$
Explanation
The integrand is continuous on the unit square, so reverse the integration order. Integrating with respect to $y$ first gives $\int_0^1x\cos(xy)dy=\sin x$. Therefore $I=\int_0^1\sin x\,dx=1-\cos1$. **A**.