Chapter 16, Problem 5RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

State the Fundamental Theorem for Line Integrals.

To determine

**To state**: The fundamental theorem of line integrals.

Explanation

Consider a smooth curve *C* which is given by vector
*f* is differentiable and the gradient of *f*
*C*. According to the Fundamental theorem of line integrals, the line integral over the curve *C* is,

Here,

*a* and *b* are the limits of domain.

The Fundamental theorem of line integrals is applicable for a conservative vector field.

In case the function *f* has two variables, consider the start point of curve *C* as

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