Triple Integrals Find the mass of the solid S made out of material with density f.

Question

Find the mass of the solid S made out of material with density f in maple. S is a ball bounded by the sphere (x−2)^2+(y+3)^2+(z−4)^2 =5; f(x, y, z)=x^2y^2.

How can I solve without changing it into a cylindrical coordinate? I tried the following but I am not sure if I did it right. z limit from 4-sqrt(5-(x-2)^2 -(y+3)^2) to 4+sqrt(5-(x-2)^2 -(y+3)^2) y limit from 3-sqrt(5-(x-2)^2) to 3+sqrt(5-(x-2)^2) and x limit from -3 to 7.

Answer 1

Check this for mistakes on my part...

restart;

VectorCalculus:-int(x^2*y^2,
                    [x,y,z] = Sphere(<2,-3,4>,sqrt(5)));

         2320     (1/2)
         ---- Pi 5     
          7            

Int(x^2*y^2,
    [ z = 4-sqrt(5-(x-2)^2-(y+3)^2) .. 4+sqrt(5-(x-2)^2-(y+3)^2),
      y = -3-sqrt(5-(x-2)^2) .. -3+sqrt(5-(x-2)^2),
      x = 2-sqrt(5) .. 2+sqrt(5) ]):

 simplify(value(%));

         2320     (1/2)
         ---- Pi 5     
          7