a.
To find : the approximate value of integral with the specified value of n .
a.
Answer to Problem 8E
the approximate value of integral by trapezoidal rule is
Explanation of Solution
Given information :
The integral is
Formula used : trapezoidal rule:
Where
Calculation : by using trapezoidal rule,
Since
So,
Since
Now the value is
So the approximate value of integral by trapezoidal rule is
b.
To find : the approximate value of integral with the specified value of n .
b.
Answer to Problem 8E
the approximate value of integral by midpoint rule is
Explanation of Solution
Given information :
The integral is
Formula used:
Midpoint rule:
Calculation: by using midpoint rule,
Since
So,
The midpoint of the four subintervals are
So by the midpoint rule:
So, the approximate value of integral by midpoint rule is
c.
To find : the approximate value of integral with the specified value of n .
c.
Answer to Problem 8E
the approximate value by simpson’s rule is
Explanation of Solution
Given information :
The integral is
Formula used:
Simpson’s rule:
Where n is even and
Calculation: by using simpson’s rule,
Since
So,
Thus, the approximate value by simpson’s rule is
Chapter 5 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning