I've been given the following problem to solve:
The region above the interval [1, 2] of the x-axis and below the curve y = (3x - x^2 - 2)^1/2 is rotated around the x-axis giving a solid of revolution. This solid of revolution has density, depending only on the x-coordinate, this is given by p(x) = 3x. Where is the centre off mass of this solid?
So far I've worked out the following (which may or may not be correct):
I think I'm on the right track, but I don't know how I can take this information about the volume and apply it to the density function to produce the mass, then calculate the centre of mass. Any help would be greatly appreciated.