GATE ECE 2023 | Question: 45

Question

The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).

 

Answer 1

From figure

$y=-x+2=x$

so $x=-x+2$

$2x=x$

$x=1$

similarly from $y=x+2$ and $y=-x$

$x=-1$

from figure y is between $0$ and $2$

$\int \int_R  xy\,dx dy= \int_0^2\int_{-1}^1xy\,dxdy=\int_0^2 y[\frac{x^2}{2}]_{-1}^1\,dy=\int_0^2 0\,dy=0$