Volume of the Solid involving Hyperbolic functions

[Strategist102]

Homework Statement

The area bounded by y=2 coshx, the x-axis, the y-axis, and the line x=4 is revolved about the x-axis. Find the volume of the solid generated.

Homework Equations

I sliced the area along the axis of revolution. That is the strip is dx. So the equation necessary is pi(R^2-r^2) from the limits of integration (0,4)

The Attempt at a Solution

pi$$\int((2cosh(x))^2-16)$$ from 0 to 4
I am uncertain if my logic is sound. Any feedback would be appreciated.

 

[Strategist102]

I think it would be best to use disks to solve this problem. If I were to use shells the slicing would be awkward. Can anyone give me some pointers?

 

[cronxeh]

Why not just integrate pi*(2*cosh(x))^2 dx from 0 to 4

Your vertical strip is just between y=2*cosh(x) and y=0. So pi(R^2-0). x=4 is just the boundary condition, your limits are from x=0 to x=4

 

[Strategist102]

Thank you. The thought occurred to me that I could just integrate that. And the logic behind that seems sound by my accounts. I just needed some additional feedback.