Gverify that the divergence theorem is true for the vector field f on the region e. f(x, y, z) = z, y, x , e is the solid ball x2 + y2 + z2 ≤ 36

Converting to spherical coordinates, we have



On the other hand, we can parameterize the boundary of by



with and . Now, consider the surface element





So we have the surface integral - which the divergence theorem says the above triple integral is equal to -




as required.