posted by Sam .
Consider the region bounded by the parabola y=x^2 and the line y=16 .
(a) What is the volume of the solid generated when revolving this region about the line y=16 ?
first sketch it. then determine where the y=16 line intersects (-4,16)(4,16)
Now, lets integrate from the parabola to the line
area= INT (16-x^2)dx from x=-4 to 4
area= [16x-1/3 x^3] over the limits
area= 16*4-1/3 4^3 - 16(-4)+1/3 (-4)^3
=2(16*4 - 1/3 4^3)
and you can finish it.
You could have recognized symettry, and just integrated from x=0 to 4, then doubled the area.