(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
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