calculus
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
dArea=dx*(16y)=(16x^2)dx
area= INT (16x^2)dx from x=4 to 4
area= [16x1/3 x^3] over the limits
area= 16*41/3 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.