Using triple integrals to find centre of gravity of an object with varying density
i have a really hard homework question where i have spent hours trying to figure it out.
the question is;
i have done some research on the web and found that the centre of gravity of an object with varying density is cg * W = g * SSS x * rho(x,y,z) dx dy dz where cg is center of gravity, W is weight(which i dont have), g is gravity(which is also not specified), SSS indicates a triple integral with respect to dx,dy,dz and rho(x,y,z) is the object density.
find the centre of gravity of a solid bound by
(for y>=0), z=0, y=0, x=-1 and x=1 which has a mass density of
i asked my lecturer about it and this is what she replied;
You need an integral to find the mass (this will be just a number, not a function). You then need an integral to find the x-coordinate of the centre of gravity (this will also be just a number, not a function). Then one for the y-component and then one for the z-component. So in total, you should do 4 triple integrals.please help as i cannot figure it out.