Hey, I just noticed that you referenced the book for the solution to problem 10. That one's actually got a simple, if ass-backwards approach thanks to the divergence theorem. No word at this computer, sorry for the ascii. Consider that _ _ dS = ndS and _ 2 2 2 n = grad( f = x + y + z ) = <2x,2y,2z> And the unit normal is just 1/2 of that;
_ _ _ 2 So find a function F s.t. F . n = x _ Simple! F = _ Notice that div F = 1 // 2 // _ _ /// _ /// || x dS = || F . dS = ||| div F dV = ||| 1 dV // // /// /// S S B B And that's just the volume of a unit sphere; 4pi/3! I figured that was the point of the problem... perhaps the book should have revisited that problem to show how much easier life can be with the divergence theorem?