Question

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

f(x)=√x-4, y=0, x=13.

Answer 1

`40.5 \pi` cubic units

Explanation:

Given is a function exponential as

`f(x) =√( (x-4))`

The region bounded by the above curve, y =0 , x =13 is rotated about x axis.

the intersection point is at x=4

The limits for x are 4 and 13

The volume when rotated through x axis is found by

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

Here a = 4 and b =13

volume =
`\pi\int\limits^13_(4) x-4} \, dx`

=
`\pi ((x^2 )/(2)-4x )\\= (\pi)/(2) (153-72)\\= 40.5 \pi`.cubic units