   Chapter 4.2, Problem 13E

Chapter
Section
Textbook Problem

# If you have a CAS that evaluates midpoint approximations and graphs the corresponding rectangles (use RiemannSum or middlesum and middlebox commands in Maple), check the answer to Exercise 11 and illustrate with a graph. Then repeat with n = 10 and n = 20.

To determine

To check:

The answer to Exercise 11 and illustrate with a graph using a CAS

Explanation

1) Concept:

Use CAS to evaluate midpoint approximation and graphs the corresponding rectangles by using the given commands in Maple.

2) Given:

Exercise (11):

02xx + 1dx,  n=5

3) Calculation:

i) n = 5

Use the following command in Maple

with(Student[Calculus1])

RiemannSum(x/(x+1), 0 2,partition=5, method=midpoint, output=plot)

The graph is shown below.

The approximate area = 0.9071

ii) n =10

Use the following command in Maple

with(Student[Calculus1])

RiemannSum(x/(x+1), 0

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