1) Use the triple integral to find the volume of the solid bounded above and below by the sphere x^2 + y^2 + z^2 = 9 and cylinder x^2 + y^2 = 4
2) Find the work done by a force F(x,y,z) = (x+y)i + (xy)j - (z^2)k acting on a particle that moves along the line segment from (0,0,0) to (1,3,1) and then along the line segment from (1,3,1) to (2,-1,4)
3) Let S be the first-octant portion of the paraboloid z= x^2 + y^2 that is cut off the by the plane z=4. If F(x,y,z) = (x^2 + z)i + (zy^2)j + (x^2 + y^2 + z)k, find the flux of F through S.
If you could help me with any of these problems much would be appreciated. If you could show your work then that would be great too! Thanks!