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.
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!