We wish to define the average value Av(f ) of a continuous function f along a curve C of
Chapter 16, Problem 71(choose chapter or problem)
We wish to define the average value Av(f ) of a continuous function f along a curve C of length L. Divide C into N consecutive arcs C1,..., CN , each of length L/N, and let Pi be a sample point in Ci (Figure 25). The sum 1 N i=1 f (Pi) may be considered an approximation to Av(f ), so we define Av(f ) = lim N 1 N i=1 f (Pi) Prove that Av(f ) = 1 L C f (x, y, z) ds 11 Hint: Show that L N i=1 f (Pi) is a Riemann sum approximation to the line integral of f along C.
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