   Chapter 16, Problem 7RCC

Chapter
Section
Textbook Problem

State Green’s Theorem.

To determine

To state: The Green’s theorem.

Explanation

The Green’s theorem demonstrates a relationship between the line integral of vector field over curve C and a double integral of curve C. The Green’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,

CPdx+Qdy=D(QxPy)dA

Here,

Py is continuous first-order partial derivative of P,

Qx is continuous first-order partial derivative of Q, and

P and Q have continuous partial derivatives

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