Area of the region bounded by the curve \(y^2=4x\), y - axis and line \(y=3\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{9}{4}\) sq. units
The region lies between the curve and the y-axis, from y = 0 (where the curve meets the y-axis, at the origin) up to y = 3. So it is taken in horizontal strips, with x as a function of y:
\( \displaystyle x = \frac{y^2}{4} \)
\( \displaystyle \text{Area} = \int_0^3 \frac{y^2}{4}\,dy \)
\( \displaystyle = \left[\frac{y^3}{12}\right]_0^3 \)
\( \displaystyle = \frac{27}{12} = \frac{9}{4} \text{ sq. units} \)
NCERT (2026-27 edition):
Area under Simple Curves
