Chapter 16.2, Problem 15E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**15.** `∫`

_{C}*z*^{2} *dx* + *x*^{2} *dy* + *y*^{2} *dz*, *C* is the line segment from (1, 0, 0) to (4, 1, 2)

To determine

**To Evaluate:** The line integral

Explanation

**Given data:**

The given curve

**Formula used:**

Write the expression to find the parametric equations for a line through the point

Write the expression to find direction vector

Consider the points

**Calculation of direction vector:**

Substitute 4 for

**Calculation of parametric equations of the curve:**

Substitute 1 for

Consider the limits of scalar parameter

Find the expression

Substitute

Find

Differentiate on both sides of the expression

Find the expression

Substitute

Find

Differentiate on both sides of the expression

Find the expression

Substitute

Find

Differentiate on both sides of the expression

Sect-16.1 P-1ESect-16.1 P-2ESect-16.1 P-3ESect-16.1 P-4ESect-16.1 P-5ESect-16.1 P-6ESect-16.1 P-7ESect-16.1 P-8ESect-16.1 P-9ESect-16.1 P-10E

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