Use Green’s Theorem in the form of Equation 13 to prove Green’s first identity : where D and C satisfy the hypotheses of Green’s Theorem and the appropriate partial derivatives of ƒ and g exist and...

Use Green’s Theorem in the form of Equation 13 to proveGreen’s first identity:

whereD andC satisfy the hypotheses of Green’s Theorem and the appropriate partial derivatives of ƒ andg exist and are continuous. (The quantity ∇
g . n = D_n

g occurs in the line integral. This is the directional derivative in the direction of the normal vectorn and is called thenormal derivativeofg.)