Chapter 16, Problem 37RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Let F(*x*, *y*, *z*) = (3*x*^{2} *yz* – 3y) **i** + (*x*^{3}*z* – 3*x*) **j** + (*x*^{3}*y* + 2*z*) **k**

Evaluate ∫_{C}**F •** *d***r**, where *C* is the curve with initial point (0, 0, 2) and terminal point (0, 3, 0) shown in the figure.

To determine

**To evaluate:** The value of
*C* is the curve with initial point

Explanation

**Given data:**

**Formula used:**

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

Find the value of

Substitute

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

Consider

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

Substitute

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

Integrate equation (4) with respect to *x*.

Apply partial differentiation with respect to *y* on both sides of equation (7).

Consider the value of

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