Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curve about the x-axis.
y = 4x^2, 2x+y=6
I have set these two equations equal to each other and found their points of intersection is (-3/2, 9) and (1,4). Since this is rotating about the x-axis dy should be used.
So I have set up the problem as
However when I integrate that the answer is not like the back of the book. The answer according to the back of the book is (250pi)/3.
What am I doing wrong? I could get that answer easily with the disk/washers method but I don't know where I went wrong on doing this with the cylindrical shells. Please help me. Thank you.
Notice that when y=4 the curve that is on top changes. Remember that we are integrating with respect to y, so the curve "on top" is the one on the right. Notice the blue and red lines in the attachment.