GATE 2026 EC – Question 61
Consider the square region $R$ in the X-Y plane as shown with the dark shading in the Figure. The value of $\iint_R(x^2+y^2-1)\,dx\,dy$ is ________. (rounded off to two decimal places)
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Correct answer: 0.66 to 0.68
Explanation
Shift $u=x-1$, so the region is $|u|+|y|\le1$ with area 2. The integrand becomes $u^2+2u+y^2$ and the odd term integrates to 0. Since $\iint u^2=\iint y^2=1/3$, the result is $2/3\approx0.67$.