Area bounded by the curve \( y^2=4x \) and the lines \( y=2 \) and \( x=0 \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{2}{3} \) square units.
The region lies between the y-axis and the parabola, from y = 0 to y = 2. It is simplest to integrate with respect to y, using \( x=\frac{y^2}{4} \).
\( \displaystyle \text{Area}=\int_0^2\frac{y^2}{4}\,dy \)
\( \displaystyle =\frac{1}{4}\left[\frac{y^3}{3}\right]_0^2 \)
\( \displaystyle =\frac{8}{12}=\frac{2}{3}\ \text{square units} \)