- #1

PaulingL

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## Homework Statement

The volume of a solid obtained by rotating the region enclosed by

x=0, y=1, x=y^5 about the line y=1

can be computed using the method of disks or washers via an integral.

## Homework Equations

V= ∏[itex]\int[/itex](R^2-r^2)dx

## The Attempt at a Solution

I have attempted this problem many times, and have come up with a lot of different approaches. When I drew this out, it seemed like I needed to calculate the entire cylinder, and then subtract the 'bowl' from the inside.

This gave me V= ∏[itex]\int[/itex](1^2-(1-(x^(1/5)))^2)

I know that it needs to be integrated with respect to x (dx) and that the limits of integration are from 0 to 1 because I got those correct.

I have also thought of the problem as a simple disk problem using V=∏[itex]\int[/itex](x^(1/5))^2 to no avail.

I would really appreciate any help!

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