   Chapter 4.2, Problem 16E

Chapter
Section
Textbook Problem

# Use a calculator or computer to make a table of values of left and right Riemann sums L n and R n for the integral ∫ 0 2 1 + x 4 d x with n= 5, 10, 50, and 100. Between what two numbers must the value of the integral lie? Can you make a similar statement for the integral ∫ − 1 2 1 + x 4 d x ? Explain.

To determine

To make:

A table of the values of the left and the right Riemann sums Ln and Rn for the given integral with n = 5, 10, 50 and 100 and then decide between what two numbers the value of the integral must lie.

Explanation

1) Concept:

Use a calculator or computer to make a table of the values of theleft and theright

Riemann sums,Ln and Rn, for the integral 021+x4 dx with n=5, 10, 50 and 100

2) Given:

021+x4 dx with n=5, 10, 50 and 100 and -121+x4 dx

3) Calculation:

By using a calculator or computer,  prepare a table of  the values of the left and the right

Riemann sums Ln and Rn as shown below.

 n Ln Rn 5 3.080614 4.329856 10 3.354110 3.978731 50 3.591540 3.716464 100 3.622383 3

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