Let P(x,y,z),Q(x,y,z), and R(x,y,z) have continuous first partial derivatives on R^(3). Let C be a closed smooth curve without self intersection, let S be a smooth surface which can be injectively projected onto the xy-plane and whose boundary is C, and let hat(n) be the unit normal to S chosen thusly: If when traversing C,S is on the left, then

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Let P(x,y,z),Q(x,y,z), and R(x,y,z) have continuous first partial derivatives on R^(3). Let C be a closed smooth curve without self intersection, let S be a smooth surface which can be injectively projected onto the xy-plane and whose boundary is C, and let hat(n) be the unit normal to S chosen thusly: If when traversing C,S is on the left, then put hat(n) on that side. If when traversing C,S is on the right, then put hat(n) on the other side. (Think right hand rule.) Use Green's Theorem to prove that o int_C Qdy=_(S)((delQ)/(delx)(hat(k))-(delQ)/(delz)(hat(i)))*hat(n)dS

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