Sketch the region bounded by the lines $2x + y = 8, y = 2, y = 4$ and the y-axis. Hence, obtain its area using integration.

5

The correct answer is Option (2) → 5

$2x+y=8$

$y=2$

$y=4$

$\text{Required Area} = \int_{2}^{4} x \, dy = \int_{2}^{4} \frac{8-y}{2} dy$

$= \left[ 4y - \frac{y^2}{4} \right]_{2}^{4} = [16 - 4] - [8 - 1]$

$\text{Required Area} = 5 \text{ unit}^2$