Hi s3a,
I think you want to solve this using shells rather than washers.
You haven't correctly set up the surface areas of the cylinders.
For the cylinders whose heights go from one end of the curve to the other,
corresponding to y=0 to y=4,
Then the vor for that region is
This works out to be about
For the upper region, where the cylinder height stretches between the line and curve
x for the curve is negative here always.
The vor of this region is
Evaluating this yields about
The sum of the 2 volumes of revolution is