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.