Question

Verify the Divergence Theorem when the vector-field F has the form,\[F(x,y,z)=a(xy^2i+yx^2j)+x^2cos(\pi z)k, \ a \gt 0,\] and D is the cylinder,\[x^2 + y^2 \le 1, 0 \le z \le \frac{1}{2}.\]