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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Do part d and e
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
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
Simpson's rule and error s grivoll
nolivib
ii)
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 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 Simpson's rule and error s grivoll nolivib ii) 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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