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)=1/3x+2, y=0, x=1, x=3.

Answer 1

\pi \frac{7}{(11) cubic units

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.

`f(x)=(1)/(3x+2 ) , y=0, x=1, x=3.`

Thus limits for x are 1 and 3

Here
`y^2 = (1)/((3x+2)^2)`

Volume of the solid when f(x) is rotated about x axis from a to b is

`\pi \int\limits^a_b {f(x)^2} \, dx`

Substitute to get

`\pi \int\limits^3_1{(1)/((3x+2)^2)\, dx`

`4\pi{ (-1)/((3x+2))^3_1`

cubic units

cubic units