Question

a) Using the following table of values, find approximately by Simpson’s rule, the arc  ength of the graph y=\frac{1}{x} between the points (1, 1) and \left ( 5,\frac{1}{5} \right )

x 1 2 3 4 5

 

12 Mar 2024
Answer :
Word Count : 361
To solve this problem using Simpson’s rule for numerical integration, we first need to understand the formula and how to apply it with the given data. ### Simpson’s Rule Formula: The formula for Simpson’s rule is: \[ S = \frac{h}{3} \left( f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + \cdots + f(x_n) \right) \] Where: - \( h \) is the width of each interval: \( h = \frac{b - a}{n} \), with \( a \) and \( b \) as the limits of integration and \( n ____ _________ _______ ____ _________ __________ ______ _____ ________ _____.
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