
Perform the same computation as in Sec. 24.4, but use the following equations:
Use 4-, 8-, and 16-segment trapezoidal rules to compute the integral.

To calculate: The work done for the given equations of
Answer to Problem 35P
Solution:
The value of
The value of
The value of
Explanation of Solution
Given Information:
The given expressions are as follows,
Work done in integral form (Refer Sec. 24.4)
If the direction between the force and displacement changes between initial and final position, then the work done is written as,
Here,
Formula Used:
Multiple Segment Trapezoidal Rule.
Calculation:
Calculate the work done.
Substitute the value of
Apply 4-Segment Trapezoidal rule.
Calculate the value of
Divide the interval from
So, the value of x after each iteration is
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Similarly, calculate for
Calculate the solution using Trapezoidal rule,
Substitute function values from above table for
Hence, the value of
Apply 8-Segment Trapezoidal rule.
Calculate the value of
Divide the interval from
So, the value of x after each iteration is
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Similarly, calculate
Calculate the solution using Trapezoidal rule,
Substitute function values from above table
Hence, the value of
Apply 16-Segment Trapezoidal rule.
Calculate the value of
Divide the interval from
So, the value of x after each iteration is,
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Calculate
Similarly, calculate
Calculate the solution using Trapezoidal rule,
Substitute function values from above table for
Hence, the value of
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Chapter 24 Solutions
Numerical Methods for Engineers
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