Chapter 16.5, Problem 33E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

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 *f* and *g* exist and arc continuous. (The quantity ∇*g* · **n** = *D _{n} g* occurs in the line integral. This is the directional derivative in the direction of the normal vector

To determine

**To prove:** The Green’s first identity.

Explanation

Consider the expression of second vector form of Greenâ€™s Theorem.

As the

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