(a)
To find:
The approximate value of integral by using the trapezoidal rule for the given condition.
Answer to Problem 1EA
Solution:
The approximate value of integral by using the trapezoidal rule for the given condition is 46.
Explanation of Solution
Given:
The given condition is:
Approach:
Trapezoidal Rule:
Let f be a continuous function on
Calculation:
Consider the given function,
We calculate the discharge during a 24-hour period.
Hence, the total daily discharge is:
Then,
The corresponding function values will be calculated as below:
0 | 3 |
4 | 3.5 |
8 | 2.5 |
12 | 1.0 |
16 | 5.0 |
20 | 1.0 |
24 | 3.0 |
Substitute the value in the formula, we get:
Hence, the approximate value of integral by using the trapezoidal rule for the given condition is 46.
(b)
To find:
The approximate value of integral by using the Simpson’s rule for the given condition.
Answer to Problem 1EA
Solution:
The approximate value of integral by using the Simpson’s rule for the given condition is
Explanation of Solution
Given:
The given condition is:
Approach:
Simpson’s Rule:
Let f be a continuous function on
Calculation:
Consider the given function,
Then,
The corresponding function values will be calculated as below:
0 | 3 |
4 | 3.5 |
8 | 2.5 |
12 | 1.0 |
16 | 5.0 |
20 | 1.0 |
24 | 3.0 |
Substitute the value in the formula, we get:
Hence, the approximate value of integral by using the Simpson’s rule for the given condition is
Want to see more full solutions like this?
Chapter 8 Solutions
Calculus For The Life Sciences
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning