Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, and y=5+x^5 about the y-axis

Question

Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x^5 about the y-axis.

Answer 1

https://www.desmos.com/calculator/i7ulzzocli

If the axis of revolution was instead y= 5 for example, the definite integral would look quite a bit different (because the average radius would be (5-x) instead of just x.

The shell method is referable to the disk/washer method because for disk method 2 separate integrals would have to be set up one of which would require outer radius - inner radius.

Here is a url for using the washer method:

https://www.desmos.com/calculator/ju7vhppjlu