Chapter 16, Problem 7RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Evaluate the line integral.

**7.** ∫_{C} xy dx + y^{2} *dy* + *yz dz*, *C* is line segment from (1,0, −1), to (3,4, 2)

To determine

**To Evaluate:** The line integral
*C* is the line segment from

Explanation

**Given data:**

The line segment is given as follows.

**Formula used:**

Write the expression vector representation of line segment.

Here,

Write the expression to evaluate the line integral for a function

Here,

*C* and

*C*.

Write the required differential and integration formulae to evaluate the given integral.

Find parametric representation of line segment for *x*-coordinate using equation (1).

Substitute

Differentiate the equation with respect to

Find parametric representation of line segment for *y*-coordinate using equation (1).

Substitute

Differentiate the equation with respect to

Find parametric representation of line segment for *z*-coordinate using equation (1).

Substitute

Differentiate the equation with respect to

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