Volume using Cylindrical Shells

[silverbell]

Homework Statement

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 4+3x-x^2 and y+x=4 about the y-axis. Below is a graph of the bounded region.

Homework Equations

V = ∫ a to b 2 pi x f(x)

The Attempt at a Solution

∫from 0 to 4 2 pi (4-x)(4)

∫from 0 to 4 2 pi (16-4x)

∫ [16-4(4) - (16- 4(0))]

0 - 12

-12

I'm not exactly sure how to come about this problem with cylindrical shells.

 

[Mark44]

Homework Statement

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 4+3x-x^2 and y+x=4 about the y-axis. Below is a graph of the bounded region.

Homework Equations

V = ∫ a to b 2 pi x f(x)

The Attempt at a Solution

∫from 0 to 4 2 pi (4-x)(4)

∫from 0 to 4 2 pi (16-4x)

∫ [16-4(4) - (16- 4(0))]

0 - 12

-12

I'm not exactly sure how to come about this problem with cylindrical shells.

Your relevant equation is right, but in your integral, you forgot the radius factor, x.

$$2\pi \int_0^4 x(4x - x^2)dx$$

You can see the LaTeX I used by clicking the integral above.

 

[SammyS]

Draw a graph. Where do those curves intersect?