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 1
The correct answer is Option (1) → \(\displaystyle\frac{9}{4}\)
The parabola \(y^2 = 4x\) touches the y-axis at the origin. The region lies between the y-axis and the curve, from y = 0 up to y = 3, so the area is taken along the y-axis, with \(x = \frac{y^2}{4}\):
\( \displaystyle \text{Area} = \int_{0}^{3} x\,dy = \int_{0}^{3} \frac{y^2}{4}\,dy \)
\( \displaystyle = \frac{1}{4}\left[\frac{y^3}{3}\right]_{0}^{3} \)
\( \displaystyle = \frac{1}{4} \times 9 = \frac{9}{4} \)
NCERT (2026-27 edition):
Area under Simple Curves
