A student observes an open-air honeybee nest on the branch of a tree, whose plane figure is parabolic shape given by $x^2 = 4y$. Then the area (in square units) of the region bounded by parabola $x^2 = 4y$ and the line $y = 4$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{64}{3}$
The required region is symmetric about the y-axis.
So, required area (in sq. units) is:
$= 2 \int\limits_{0}^{4} x \, dy = 2 \int\limits_{0}^{4} 2\sqrt{y} \, dy = 4 \left[ \frac{y^{\frac{3}{2}}}{\frac{3}{2}} \right]_{0}^{4} = \frac{64}{3}$