   Chapter 4.R, Problem 1CC

Chapter
Section
Textbook Problem

# (a) Write an expression for a Riemann sum of a function f on an interval [ a , b ] . Explain the meaning of the notation that you use.(b) If f ( x ) ≥ 0 , what is the geometric interpretation of a Riemann sum? Illustrate with a diagram.(c) If f ( x ) takes on both positive and negative values, what is the geometric interpretation of a Riemann sum? Illustrate with a diagram.

To determine

(a)

To write:

An expression for a Riemann sum of a function f on interval [a, b] and explain the meaning of notation

Explanation

1) Concept:

The definition of Riemann sum

2) Calculation:

If f is a function defined for axb, we divide the interval [a, b] into n subintervals of equal width x=b-an then Riemann sum is given by

Rn=i=1nf(xi*)x

Where, xi*

To determine

(b)

To explain:

The geometric interpretation of Riemann sum when fx0 with diagram.

To determine

(c)

To explain:

The geometric interpretation of the Riemann sum when fx takes both positive and negative values with the help of the diagram

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