IGNOU MTE 10 2018 - Using the following table of values, find approximately by Simpson&rsq

Question

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

x	1	2	3	4	5
$\sqrt\frac{{1+x^4}}{x^4}$	1.414	1.031	1.007	1.002	1.001

14 Feb 2018

Answer :

Word Count : 153

Simpson’s 1/3 rule for $n$ subintervals (even) is: $$ \int_{x_0}^{x_n} f(x) dx \approx \frac{h}{3} \left[ f_0 + 4(f_1 + f_3 + \dots) + 2(f_2 + f_4 + \dots) + f_n \right] $$ Here, $x_0

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x	0.1	1.2	2.4	3.9
f(x)	3.41	2.68	1.37	-1.48