Let denote the sphere of radius r with center at the origin, oriented with outward normal. Suppose F is of class on all of and is such that for some fixed constants a and b.

a) Compute , where . Your answer should be in terms of a and b.

b) Suppose, in the situation just described, that for some vector field G of class . What conditions does this place on the constants a and b?

So I see that the integral is going to be over the region between the spheres of radius 5 and radius 7, but how should I proceed given that F is not explicitly defined?