Can the Disc Method Be Applied When Rotating Around y=x?

[flyers]

In my Cal 2 class we learned the disc method to rotate an area around an axis to obtain a volume. However we only rotated a function around either the x-axis or y axis. Let's say I take the function y=x²and y=x from the interval 0 to 1 and I want to rotate the area between these functions around the line y=x, can this be done? My teacher said something about tranforming the equations into standard form but also said we are not looking at these types of problem in my course.

 

[HallsofIvy]

The radius of your "disk" would be the line perpendicular to the axis of rotation- and that might be hard to find. Also the differential in the integral would not be "dx" or "dy" but some combination. Your teacher is probably right that the best method would be to transform the coordinate system.