The area bounded by the curve \( y^2=2x \) and the lines \( y=2,y=4 \) and \( y \)-axis, is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 28/3 sq. units
The region is bounded by horizontal lines and the y-axis, so horizontal strips are used and the integration is with respect to y. From the curve, \( x=\frac{y^2}{2} \).
\( \displaystyle \text{Area}=\int_{2}^{4}x\,dy \)
\( \displaystyle =\int_{2}^{4}\frac{y^2}{2}\,dy \)
\( \displaystyle =\left[\frac{y^3}{6}\right]_{2}^{4} \)
\( \displaystyle =\frac{64-8}{6} \)
\( \displaystyle =\frac{28}{3}\ \text{sq. units} \)