i have a really hard homework question where i have spent hours trying to figure it out.

the question is;find the centre of gravity of a solid bound by $\displaystyle z=1-y^2$ (for y>=0), z=0, y=0, x=-1 and x=1 which has a mass density of $\displaystyle rho(x,y,z)=yz$ grams/m^3.

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.

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.