Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.

Answer 1

the curves intersect at (0,0) and (6,36)

using washers of thickness dx, we have

v = ∫[0,6] π(R^2-r^2) dx
where R=6x and r=x^2
v = ∫[0,6] π(36x^2-x^4) dx = 5184π/5

To check, try using shells of thickness dy:

v = ∫[0,36] 2πrh dy
where r=y and h=√y-y/6
v = ∫[0,36] 2πy(√y-y/6) dy = 5184π/5

Answer 2

How did u get all of that