The area (in sq. units) of the region bounded by the curve \(x = y^{2}+1\), the y-axis and the lines y = 0 and y = 2 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{14}{3}\)
On the curve \(x = y^{2}+1 \ge 1\), so the curve lies to the right of the y-axis. The region is bounded by horizontal lines, so it is easier to integrate with respect to y:
\( \displaystyle A = \int_{0}^{2}(y^{2}+1)\,dy \)
\( \displaystyle = \left[\frac{y^{3}}{3}+y\right]_{0}^{2} \)
\( \displaystyle = \frac{8}{3}+2 = \frac{14}{3} \)