Use the method of cylindrical shells to find the volume of the solid rotated about the line given the conditions:
Look at the picture.
Let us keep things positive.
Now you are rotating about
Let us shift the coordinate axes to the right 1 unit.
That means replace for .
Thus, your new curve is,
And you are rotating this time about the y-axis becase we shifted the curve.
Thus by cylindrical shells,
Note the new limits of integration because we shifted the curve.