- #1

Agent M27

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- 0

## Homework Statement

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

[tex]y=4x-x^{2} , y=4 , x=0 [/tex]

## Homework Equations

[tex]V=2\pi\int p(x)h(x)[/tex]

from a to b

## The Attempt at a Solution

[tex]V=2\pi\int4x^{2}-x^{3}[/tex]

The equation y=4x-x^2 is the equation for an upside down parabola with its vertex at (2,2) and has roots at x=0,4. When revolving around the y-axis the bounds are from a to b which in this case ought to be 0 to 4. Instead the book gives the same integral as I have found but with the bounds from 0 to 2, I have been banging my head against the wall on this one for too long, any ideas? Thanks in advance.

Joseph