Hi,
I need to find the volume of the space between these two equations. I have learned the "Washing Machine Method" but have been told that can't be used when one of the functions is negative. Any help would be appreciated
y=2x-x^2 and y=-2x+x^2
Thank you
You have not learned the "Washing Machine Method", at least I think not. Maybe someone calls it that. Usually, we have Shells, Disks, and Washers.
Assuming we are spinning around the x-axis, the problem with the function that is negative over the given Range isn't a problem at all. You have a choice:
1) Observe the symmetry and simply ignore the negative-valued function, or
2) Rotate around the axis only through \(\displaystyle \pi\) rather than \(\displaystyle 2\pi\).
3) Think about it long enough, simply proceed as you normally would, and divide by 2.
Can you show us how to proceed if you were simply to ignore y = -2x + x^2?
Note: In my opinion, ALL THREE methods "work" for EVERY such problem. In some cases, one or two might be particularly difficult. With some experience, you will begin to see which method is easiest for a particular problem.
Note: I have always made a habit of using both shells and disks (or washers) for EVERY practice problem. Lot's of experience and an opportunity to check your own work.
