Chapter 16.3, Problem 2E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A table of values of a function *f* with continuous gradient is given. Find ∫* _{C}* ∇

*x* = *t*^{2} + 1 *y* = *t*^{3} + *t* 0 ⩽ *t* ⩽ 1

To determine

**To find:** The value of

Explanation

**Definition:**

Refer to FIGURE 1 of section 16.3 in the textbook.

Consider a smooth curve represented by a vector function

If *f* is the differentiable function of two or three variables with gradient vector
*C* then

Express
*x* and *y* coordinates.

Substitute
*x* and
*y*,

Find the *C* is smooth curve or not.

Consider
*C*. If the value of differentiation of
*C* is a smooth curve.

Differentiate equation (2) with respect to *t*.

The value of *t* limits between 0 and 1.

The value of
*C* is a smooth curve

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