Question

Help Pleeeease :3

Answer 1

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

\[y=3x^2, y=18x-6x^2\]

Answer 2

\[3x^2 = 18x-6x^2\]
\[9x^2-18x=0\]
\[9x(x-2)=0\]
\[x=0,2\]

Thus the Integral will go from 0 to 2.... But how would I set up the integral?

Answer 3

I'm not sure exactly where these functions will lie.
But I know that one is a parabola opening up,
and the other a parabola opening downward.