Chapter 16.2, Problem 16E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the line integral, where *C* is the given curve.

**16.**` ∫`

* _{C}* (

To determine

**To Evaluate:** The line integral

Explanation

**Given data:**

The given curve

The evaluation of integral

Therefore, write the line integral

Here,

**Parametric equations of**
**:**

Consider the parametric equations such that the parameters must satisfy the line segment points

The parameters are satisfied for the points

**Calculation of**
** for the line segment**
**:**

Differentiate on both sides of the expression

**Calculation of**
** for the line segment**
**:**

Differentiate on both sides of the expression

**Calculation of**
** for the line segment**
**:**

Differentiate on both sides of the expression

**Evaluation of line integral**
**:**

Substitute

Simplify the expression as follows.

**Parametric equations of**
**:**

Consider the parametric equations such that the parameters must satisfy the line segment points

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