Textbook ExpertVerified Tutor
5 Dec 2021
Given information
The given function is 
Step-by-step explanation
Step 1.
(
)
)The error bounds for Midpoint and Trapezoidal approximations are defined as follows,
Suppose for a function 
that is continuous and differentiable, 
in the interval 
then the error bounds 
and 
for Trapezoidal and Midpoint approximations respectively are given as,
that is continuous and differentiable, in the interval then the error bounds and for Trapezoidal and Midpoint approximations respectively are given as,
The error bound for the Simpson's rule is defined as follows, Suppose for a function that is continuous and differentiable, 
in the interval
that is continuous and differentiable, in the interval
then the error bound 
for Simpson's approximation is given as,
The second and fourth derivatives of the function 
are,
are,
Since, these values lie between 
and 
in the interval 
the maximum value is .
and in the interval the maximum value is .Therefore,
Therefore, the error bound for Trapezoidal rule is,
The error bound for Midpoint rule is,
The error bound for Simpson's rule is,
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1a
- Problem 1b
- Problem 1c
- Problem 1d
- Problem 2a
- Problem 2b
- Problem 3
- Problem 4a
- Problem 4b
- Problem 4c
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17a
- Problem 17b
- Problem 17c
- Problem 18a
- Problem 18b
- Problem 18c
- Problem 19a
- Problem 19b
- Problem 19c
- Problem 20
- Problem 21a
- Problem 21b
- Problem 21c
- Problem 21d
- Problem 21e
- Problem 21f
- Problem 21g
- Problem 21h
- Problem 21i
- Problem 21j
- Problem 22
- Problem 22b
- Problem 23
- Problem 24
- Problem 25
- Problem 25
- Problem 26
- Problem 26
- Problem 27a
- Problem 27b
- Problem 27c
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33a
- Problem 33b
- Problem 34
- Problem 35
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39
- Problem 40
- Problem 41
- Problem 42