   Chapter 16.3, Problem 1E

Chapter
Section
Textbook Problem

The figure shows a curve C and a contour map of a function f whose gradient is continuous. Find ∫C ∇ f · dr. To determine

To find: The value of Cfdr .

Explanation

Definition:

Refer to FIGURE 1 of section 16.3 in the textbook.

Consider a smooth curve represented by a vector function r(t) , atb .

If f is the differentiable function of two or three variables with gradient vector f is continuous on curve C then Cfdr ,

Cfdr=f(r(b))f(r(a)) (1)

Re-modify given Figure as shown in Figure 1

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