The area of the region bounded by parabola \(x^2 = 4y\), straight line \(x = 2\) and x-axis, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{2}{3}\) Sq. units
The parabola \(y = \displaystyle\frac{x^2}{4}\) touches the x-axis at the origin. The region lies under the parabola and above the x-axis, from \(x = 0\) to \(x = 2\):
\( \displaystyle \text{Area} = \int_{0}^{2} \frac{x^2}{4}\,dx \)
\( \displaystyle = \frac{1}{4}\left[\frac{x^3}{3}\right]_{0}^{2} = \frac{1}{4} \cdot \frac{8}{3} = \frac{2}{3} \)