Answer:
18 \pi cubic units
Step-by-step explanation:
Given that a region is bounded by
[tex]f(x)=√2x+1, y=0, x=1, x=4[/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^4_1 {2x+1} \, dx\\=\pi *x^2+x ^4_1\\= \pi*16+4-1-1\\=18\pi[/tex]
cubic units.
