(a)
To find : The Simpson’s rule approximations for
(a)
Answer to Problem 28E
The answer:
Explanation of Solution
Given information:
The integral is
Calculation:
To use the calculator program and get,
Therefore, the required Simpson’s rule approximations for
(b)
To find: The errors with as many decimal places with accuracy.
(b)
Answer to Problem 28E
The answer is:
10 | |
100 | |
1000 | 0 |
Explanation of Solution
Given information:
The integral is
Calculation:
From part
The exact value is:
The errors are then,
10 | |
100 | |
1000 | 0 |
(c)
To find: The pattern.
(c)
Answer to Problem 28E
The answer is:
Explanation of Solution
Given information:
The integral is
Calculation:
From part
The error for
Multiplying the number of subintervals,
times the error for
Therefore, the required pattern is
(d)
To explain: The error bound for
(d)
Answer to Problem 28E
The answer is:
Explanation of Solution
Given information:
The integral is
Calculation:
The Error bound formula for
Hence, the integral is
And,
Hence,
And
Put these into the error formula and gives:
If the number of subintervals is multiplied by 10, then
Therefore, the required error bound for
Chapter 5 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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