Concept explainers
(a)
To calculate: The value of the
(a)
Answer to Problem 14E
The value of integral is
Explanation of Solution
Given information:
The value of n=4 approximation is given below as,
Formula used:
Calculation:
To approximate
Where [a, b] is partitioned into an even number n of subintervals of equal length
Now, apply the Simpson’s rule with
So,
Now, substitute the values from given table in this equation
Conclusion:
The value of integral is
(b)
To calculate: The exact value of the integral.
(b)
Answer to Problem 14E
The value of the integral is
Explanation of Solution
Given information:
Formula used:
Calculation:
If f is continuous at every point of [a, b], and if F is any anti-derivative of f on [a, b], then
This part of the fundamental theorem is also called the integral evaluation theorem.
Now, use the above formula to find the value of integral.
If F is any anti-derivative of f then
So,
Conclusion:
The value of the integral is
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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