Concept explainers
(a)
To calculate: The value of the
(a)
Answer to Problem 28E
The value of integral is 2.00
Explanation of Solution
Given information:
The value of function is
Formula used:
Calculation:
In Simpson’s rule, to approximate
Where [ a , b ] is partitioned into an even number n of subintervals of equal length
Now,
To find integral use your calculator program of Simpson's rule approximations with
Conclusion:
The value of integral is 2.00
(b)
To calculate:The exact value of the integral is
(b)
Answer to Problem 28E
The value of the integral is 0 when n=1000
Explanation of Solution
Given information:
The value of function is
Formula used:
Calculation:
If S represents the approximation to
Here, use your calculator to find the error, error is also given by
Where Tn represents the value of integral by trapezoidal rule for different value or n
Conclusion:
The value of the integral is 0 when n =1000
(c)
To calculate:the value of error.
(c)
Answer to Problem 28E
Explanation of Solution
Given information:
The value of function is
Formula used:
The error gets multiplied
Calculation:
Observe the last column or above table, error gets multiplied approximately by 10-4
So,
Conclusion:
(d)
To find:The value of error bound.
(d)
Answer to Problem 28E
Explanation of Solution
Given information:
The value of function is
Formula used:
Calculation:
Now, use the formula for error bound
Now
So,
Hence, error bound accounts for the pattern.
Conclusion:
The error bound gets account for the pattern.
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
Calculus: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus
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