Volume of a solid using shells

[Feodalherren]

Homework Statement

Find the volume of the region bounded by the curve y=x^(1/3) and y=x rotated about the line y=1.

Homework Equations

The Attempt at a Solution

My teacher's solution is 4∏/15 . I got 11∏/210.

http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
Where am I going wrong?

 

[Mark44]

Homework Statement

Find the volume of the region bounded by the curve y=x^(1/3) and y=x rotated about the line y=1.

Homework Equations

The Attempt at a Solution

My teacher's solution is 4∏/15 . I got 11∏/210.

http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
Where am I going wrong?

You don't have a sketch of the solid of revolution, so I can't tell what you did. However, it looks like you didn't rotate the region around the line y = 1. I find that it's helpful to have a sketch of the solid, at least a cross-section of it, showing the typical volume element.