Quick question: If I have these 2 equations y = sqrtx and y = 20 - x about the x- axis, how would I put this in the volume integral form? I know the formula is v = 2pi (radius)(height) dy but how would I put this into integral form?

Answer 1

Did you sketch the region? The curves intersect at (16,4)
What is the other boundary of the region? The x-axis or the y-axis?
If the x-axis is the boundary, then
r = y and h = (20-x)-√x

If the y-axis is the boundary, then you have to split it up into two parts
v = ∫[0,4] 2πy(20-y)^2 dy + ∫[4,20] 2πy(20-y) dy