The area of the region bounded by the curve $x = 2y + 3$ and the lines $y = 1, y = -1$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $6$ sq units
We have the equations, $x = 2y + 3, y = 1$ and $y = -1$.
Required area, $A = \int_{-1}^{1} (2y + 3) \, dy$
$= \left[ \frac{2y^2}{2} + 3y \right]_{-1}^{1}$
$= [y^2 + 3y]_{-1}^{1}$
$= [1 + 3 - 1 + 3] = 6 \text{ sq. units}$