Cylindrical Shells Volume

Homework Statement

Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

x= (y^2) +1

x= 0

y=1

y=2

2∏ ∫ rh

The Attempt at a Solution

2∏ ∫ from 1 to 2 (y^2) + 1

Mark44
Mentor

Homework Statement

Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

x= (y^2) +1

x= 0

y=1

y=2

2∏ ∫ rh

The Attempt at a Solution

2∏ ∫ from 1 to 2 (y^2) + 1

Start with a sketch of the region that is being rotated. Then draw a sketch of the solid that is formed.

I drew a sketch. I'm not sure what do do about the radius part. I know y= 2 is the higher radius along the x-axis. And y= 1 is the lower radius along the x-axis. Do I subtract the radius minus function?

Mark44
Mentor
The expression for incremental volume (the volume of a thin horizontal strip that is revolved around the x-axis) is 2$\pi$ * radius * width of strip * Δy.

The radius varies from what to what?
How wide is a typical strip?