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 (1) → $\frac{2}{3}$ Sq. units
Given: Parabola $x^2 = 4y$, line $x = 2$, and x-axis ($y = 0$)
Rewrite the parabola: $y = \frac{x^2}{4}$
Required area: Area under parabola from $x = 0$ to $x = 2$
$\text{Area} = \int_0^2 \frac{x^2}{4}\, dx = \frac{1}{4} \int_0^2 x^2\, dx = \frac{1}{4} \cdot \left[\frac{x^3}{3}\right]_0^2$
$= \frac{1}{4} \cdot \left( \frac{8}{3} \right) = \frac{2}{3}$
