Let Sr denote the sphere of radius r with center at the origin, oriented with outward
Chapter 7, Problem 24(choose chapter or problem)
Let Sr denote the sphere of radius r with center at the origin, oriented with outward normal. Suppose F is of class C1 on all of R3 and is such that Sr F dS = ar + b for some fixed constants a and b. (a) Compute D F dV, where D = {(x, y,z) | 25 x 2 + y2 + z2 49}. (Your answer should be in terms of a and b.) (b) Suppose, in the situation just described, that F = G for some vector field G of class C1. What conditions does this place on the constants a and b?
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