Explain the meaning of the integral S( × F) · n dS in

Chapter 13, Problem 2E

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QUESTION:

Explain the meaning of the integral \(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} \ d S\) in Stokes’ Theorem.

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QUESTION:

Explain the meaning of the integral \(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} \ d S\) in Stokes’ Theorem.

ANSWER:

Solution 2E

The meaning of (∇F)n in Stokes’ Theorem:

        
        The stroke’s theorem says that if
is a smooth, oriented surface in  with smooth closed boundary

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