- #1

lingualatina

- 12

- 2

## Homework Statement

Find the volume of the region bounded by the curves y=3x-2, y=6-x, and the x-axis when the region is rotated around the y-axis.

## Homework Equations

Volume using cylindrical shells: 2π∫r(x)h(x)dx

## The Attempt at a Solution

I graphed the curves and then found the x-intercept of 3x-2 (which was 2/3) and the x-value of the intersection point of the two lines (which was 2). Then I set up two integrals: 2π∫x(6-x)dx from 0 to 2/3 and 2π∫x(6-x-(3x-2))dx from 2/3 to 2. When I computed and then added these, the value was 32.579, but the answer is supposed to be 33.510. Can't figure out where I went wrong: is there a problem with splitting up the integrals like that? Thanks in advance.