1) Find the area under the function f(x)= over the interval 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1) Find the area under the function f(x) =→ over the interval 1<x<2.
a)
First sketch a graph of this area and integrate the exact value of this area.
b) Find the following approximations of this area with n= 5 subdivisions and find its
actual error, Error(5), with the above exact value:
ii) Trapezoid rule and error
Midpoint rule and error
ngboj
iii) Simpson's rule and error
c) Find the following approximations of this area with n= 20 subdivisions and find its
actual error, Error(20):
i)
Trapezoid rule and error
Midpoint rule and error
ii)
Simpson's rule and error
d) Find the ratio of errors of parts b) and c). In other words find Error(5) / Error(20)?
i)
Trapezoid rule error ratio
Midpoint rule error ratio
ii)
Simpson's rule error ratio
e) What can be observed by these error ratios and the number of subdivisions n?
Transcribed Image Text:1) Find the area under the function f(x) =→ over the interval 1<x<2. a) First sketch a graph of this area and integrate the exact value of this area. b) Find the following approximations of this area with n= 5 subdivisions and find its actual error, Error(5), with the above exact value: ii) Trapezoid rule and error Midpoint rule and error ngboj iii) Simpson's rule and error c) Find the following approximations of this area with n= 20 subdivisions and find its actual error, Error(20): i) Trapezoid rule and error Midpoint rule and error ii) Simpson's rule and error d) Find the ratio of errors of parts b) and c). In other words find Error(5) / Error(20)? i) Trapezoid rule error ratio Midpoint rule error ratio ii) Simpson's rule error ratio e) What can be observed by these error ratios and the number of subdivisions n?
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