Question

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=√4x+2, y=0, x=0, x=2.

Answer 1

12\pi cubic units.

Explanation:

Given that a region is bounded by

`f(x)=√4x+2, y=0, x=0, x=2`

And the region is rotated about x axis.

We can find that here radius would be y value and height would be dx

So volume would be as follows:

If f(x) is rotated about x axis volume

=
`\pi \int\limits^b_a {y^2} \, dx \\=\pi \int\limits^2_0 {4x+2} \, dx\\=\pi *2x^2+2x  ^2_0\\= \pi*8+4\\=12\pi`

cubic units.