Question

A student observes an open-air Honeybee nest on the branch of a tree, whose plane figure is parabolic shape given by x² = 4y. Then the area (in sq units) of the region bounded by parabola x² = 4y and the line y = 4 is ______.

Options

• `32/3`

• `64/3`

• `128/3`

• `256/3`

Answer 1

A student observes an open-air Honeybee nest on the branch of a tree, whose plane figure is parabolic shape given by x² = 4y. Then the area (in sq units) of the region bounded by parabola x² = 4y and the line y = 4 is `underlinebb(64/3)`.

Explanation:

The required region is symmetric about the y-axis.

So, required area (in sq units) = `|2int_0^4 2sqrtydy| = 4[(y^(3/2))/(3/2)]_0^4 = 64/3`.