How could I find the volume between the curves y= e^3 and y=x , rotated about the x-axis? Should I be using the disk/washer method or the cylindrical method?
As stated, your problem doesn't make any sense. e^3 is a constant. So you have the straight line y = e^3, and the straight line y = x. Those are intersecting straight lines - they don't enclose any area. Could you please re-state the problem precisely?