Calculus...FUN!?

Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y = 0, y = x(6 - x) about the axis x = 0

Washer method:
V = A * h
V = pi(r2^2 - r1^2)h

(1296pi/5 is not the solution)

Answer 1

You should always draw a picture of what's going on. Here, you have a "chunk" of parabola
y=x(6-x) above the y axis from x=0 to x=6.
The washer is a horizontal sliver of the parabola of thickness dy, and the integration is carried out from y=0 to y=9.

Call the origion point A, the point (0,9)=B, the point (3,9)=C and the point (6,0)= D. One way to integrate this is to first find the volume of ABCD, where CD is the parabola from x=3 to x=6. Then find the volume of ABC, where AC is the parabola from x=0 to x=3.