Use the divergence theorem to write the volume of a threedim

Use the divergence theorem to write the volume of a three-dimensional region R a surface flux integral. Determine the sign of he divergence of the vector field in the figure below at the indicated points P_1 and P_2.

Solution

The divergence theorem states that { f(x)} as x tends to a f(x) tends to infinity. Here The volume of the three dimensional region if given by Integrate over -2 to +2 of the function f(x,y,z) = xyz and will get the volume, the range of x, y and z axis will be again -2 to +2.

the vector at P₁ = -i + j + ok

the vector at P₂ = oi - j - k