Area (in sq. units) of the region bounded by the curve \(y^2 = 4x\), y-axis and the line \(y = 3\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{9}{4}\)
The region lies between the y-axis and the parabola, from y = 0 (the vertex) up to y = 3. So integrate with respect to y, with
\( \displaystyle x = \frac{y^2}{4} \)
\( \displaystyle \text{Area} = \int_{0}^{3} \frac{y^2}{4}\,dy \)
\( \displaystyle = \frac{1}{4}\left[\frac{y^3}{3}\right]_{0}^{3} \)
\( \displaystyle = \frac{1}{4} \times 9 = \frac{9}{4} \)