Chapter 16.2, Problem 5E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**5.** ∫* _{C}* (

To determine

**To Evaluate:** The line integral

Explanation

**Given data:**

The given curve

**Formula used:**

Write the expression to evaluate the line integral with respect to arc length.

Here,

*x*-coordinate of the curve

*x*-coordinate of the curve

As the equation of parabola is

From the given two points, choose *x*-coordinates as limits to evaluate the integral

Find the expression

Substitute

**Calculation**
**:**

Write the equation of parabola as follows.

Differentiate on both sides of the expression with respect to

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

Substitute

Simplify the expression as follows.

Compute the integration part

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