Chapter 16, Problem 7RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

State Green’s Theorem.

To determine

**To state**: The Green’s theorem.

Explanation

The Greenâ€™s theorem demonstrates a relationship between the line integral of vector field over curve *C* and a double integral of curve *C*. The Greenâ€™s theorem deals with a positive orientation that is basically counter clockwise transverse direction of the curve.

Consider a positively oriented curve *C* which is piece-wise smooth, simple closed curve in plane with domain *D*. According to the Greens theorem,

Here,

*P*,

*Q*, and

*P* and *Q* have continuous partial derivatives

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