Question

What is the volume of the solid produced by revolving `f(x)=sec, x in [pi/8,pi/3]`around the x-axis?

Answer 1

Volume `V=4.140107808" "`cubic units

Explanation:

Given equation `y=sec x` and `x` is from `pi/8` to `pi/3`.

Differential volume `dv=pi*r^2*dh` for circular solid disk

In terms of our variable

`dv=pi*f(x)^2*dx`

Volume `V`

`V=int dv=int_(pi/8)^(pi/3) pi*sec^2 x*dx`

`V=pi*[tan x]_(pi/8)^(pi/3)`

`V=pi*(tan pi/8-tan pi/3`)#

`V=4.140107808" "`cubic units

God bless....I hope the explanation is useful.