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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be (a) left endpoints and (b) mid points. In each case draw a diagram and explain what the Riemann sum represents.

Chapter 4.R, Problem 1E, Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be

To determine

a)

To find:

The Riemann sum for the left endpoints with six subintervals

Explanation

1) Concept:

Definition of the Riemann sum:

i=1nfxi* x

is called as the Riemann sum

Where,

x= b-an,    xi=a+i x,    & xi*xi-1, xi

Riemann sum is the sum, of the areas of the rectangles that lie above the x-axis and the negative of the areas of the rectangles that lie below the x-axis

2) Calculation:

First, write the expression of the Riemann sum for left endpoints

Six subintervals are given, that means, n=6

By definition of Riemann sum,

i=1nfxi x=i=16fxi x

So now calculate

To determine

b)

To find:

The Riemann sum for midpoints with six subintervals

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