Area of revolution of hyperbola

[~Sam~]

Homework Statement

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the hyperbola y²−x²=4 and the lines y=0, x=3 and x=5 about the y− axis.

Homework Equations

Nothing specific...general equations

The Attempt at a Solution

So I would write it as
I was wondering if it was just 2x*pi*dx*(√4+x²) from x=3 and x=5? Or would I have to incorporate the "hole" from x=0 to x=3.

 

[tiny-tim]

I was wondering if it was just 2x*pi*dx*(√4+x²) from x=3 and x=5? Or would I have to incorporate the "hole" from x=0 to x=3.

Hi ~Sam~!

(have a pi: π )

Yes, just ∫₃⁵ 2x*π*dx*√(4+x²) …

you're "adding" the volumes of the cylindrical shells that make up the whole shape, so you only need the shells with radii from 3 to 5.