Answer:
12\pi cubic units.
Step-by-step explanation:
Given that a region is bounded by
[tex]f(x)=√4x+2, y=0, x=0, x=2[/tex]
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
= [tex]\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[/tex]
cubic units.
