Chapter 16, Problem 14RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Show that **F** is a conservative and use this fact to evaluate ∫_{C}**F** · *d***r** along the given curve.

**14. F**(*x*, *y*, *z*) = *e ^{y}*

To determine

**To show : F** is a conservative vector field and The value of
*C* is the line segment from

Explanation

**Given data:**

*C* is the line segment from

**Formula used:**

Consider the standard equation of an curl **F** for

Find the value of

Substitute

Simplify expression as follows.

Since
**F** is a conservative vector and the domain of **F** is

Thus, **F** is a conservative vector field is shown.

Consider

Write the relation between the potential function *f* and vector field

Substitute

Compare the equation (3) and equation (1).

Integrate equation (5) with respect to *y*

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