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 December 27th, 2013, 11:06 AM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Fundamental theorem of calculus for surface integrals? Hellow! A simple question: if exist the fundamental theorem of calculus for line integrals not should exist too a fundamental theorem of calculus for surface integrals? I was searching about in google but I found nothing... What do you think? Such theorem make sense? December 27th, 2013, 04:15 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Fundamental theorem of calculus for surface integrals? That may be because it is incorporated into a much more general theorem- the generalized Stokes' theorem: if is a differential form defined on a differentiable manifold then (http://en.wikipedia.org/wiki/Stokes'_theorem). That is, the integral of the differential form, over region is the anti-derivative, integrated (i.e. evaluated) over the boundary of the region . The reason why we have specific expressions for an integral on the real number line or on a path in two or three dimensions is that the boundary is just the two endpoints and in "integrating" on that boundary is just evaluating at the two endpoints and subtracting. In the case that is a two dimensional surface in three dimension, is the closed path boundary of the surface. December 27th, 2013, 07:14 PM #3 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Re: Fundamental theorem of calculus for surface integrals? But, anyway, exist a geometric explanation for the fundamental theorem of calculus for surface integral, a geometric explanation analogous to t.f.c. for line integral? Tags calculus, fundamental, integrals, surface, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post layd33foxx Calculus 3 December 12th, 2011 07:32 PM riotsandravess Calculus 3 November 25th, 2010 12:44 PM Aurica Calculus 1 June 14th, 2009 08:04 AM Aurica Calculus 1 June 10th, 2009 05:39 PM mrguitar Calculus 3 December 9th, 2007 01:22 PM

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