[CSC 335] Problem 4.9 3(c)

[Andrew J. Pounds]

I think this was the problem you all asked about in class yesterday...

You are asked to approximate the integral 
$\int_1^{\infty}\frac{\cos(x)}{x^3}dx$ using composite Simpson's rule 
with n=6.

Once I make the recommended substitution and simplify I get $\int_0^1 t 
\cos(\frac{1}{t})dt$ .  The problem here is what to do about the 
singularity at 0.  Since $\lim_{t \rightarrow 0} t \cos(\frac{1}{t}) = 
0$  I can use zero for the $f(a)$ term in the composite Simpsons rule 
formula.  In this case there is no need to expand in a Taylor polynomial.

Does that help?

-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

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