Answer:
\pi \frac{7}{(11) cubic units
Step-by-step explanation:
We have to find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.
[tex]f(x)=\frac{1}{3x+2 } , y=0, x=1, x=3.[/tex]
Thus limits for x are 1 and 3
Here [tex]y^2 = \frac{1}{(3x+2)^2}[/tex]
Volume of the solid when f(x) is rotated about x axis from a to b is
[tex]\pi \int\limits^a_b {f(x)^2} \, dx[/tex]
Substitute to get
[tex]\pi \int\limits^3_1{\frac{1}{(3x+2)^2}\, dx[/tex]
[tex]4\pi{ \frac{-1}{(3x+2)}^3_1[/tex]
[tex]4\pi \frac{-1}{(11)-\frac{-1}{(4)[/tex] cubic units
[tex]\pi \frac{7}{(11)[/tex] cubic units
