The problem is the following: I need to find the mass, moments along the axis and the center of mass of the tetrahydron (centroid) with vertecies (-1,0,0) (1,0,0) (0,1,0) and (0,-1,0) and (0,0,2) basically it has a square base with an area of 4 and height 2 units. You are also given the density function of the solid: P(x,y,z) = absX + absY +absZ where (X,Y,Z) are variables Using triple integrals its really easy to find the volume or you can just find it at sight area of base times height however when integrating the density function over that volume I suspect that i have to divide the integral in four different parts since x and y can be either negative or positive while z is always positive so its absolute value will be z at all times. I was wondering if this approach is right and if it is would the limits of integration for all four different integrals be different and how would i go by finding them? Plus once the integral of the mass is found i suspect that the moments along each axis Mxy Myz and Mxz will be easier to find by just plugging in each corresponding varialbe in the integrand however i am not quite sure if i would plug in each corresponding variable in all four integrals or just in some of them....????? I hope someone can help!