GATE 2023 EC – Question 55
The value of the integral $\iint_Rxy\,dx\,dy$ over the region $R$, given in the figure, is ________ (rounded off to the nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0
Explanation
The region is the diamond with vertices $(0,0),(1,1),(0,2),(-1,1)$, which is symmetric about the $y$-axis. The integrand $xy$ is odd in $x$, so the contributions from $x>0$ and $x<0$ cancel exactly: the integral is 0.