[CSC 335] Section 4.9 Problems

[Andrew J. Pounds]

On 10/19/13 13:48, Levi M Mitze wrote:
> Hello again, Dr. Pounds.
>
> I'm having some difficulty understanding what to do for problem 3 from 
> section 4.9. I figured I was supposed to follow a procedure similar to 
> all the examples in the section, but there doesn't seem to be a way to 
> get the function (after inverting the variable [t = 1/x]) into a form 
> such that the numerator is a function that can be used to form a 
> Taylor polynomial. Am I just supposed to perform the inversion and 
> then approximate the integral using Composite Simpson's (and not worry 
> about Taylor polynomials)? What about part c and problem 4?
>
> Sorry for all the questions,
>
> Levi

No Taylor polynomial needed here.  Look at the paragraph around around 
and including equation 4.47 in your text. If I want to integrate

$\int_1^{\infty} \frac{1}{1 + x^4} dx$

I can use the substitution provided and convert it to the integral

$\int_0^1 t^{-2} \left[ \frac{1}{1+\left( \frac{1}{t} \right)^4} \right 
] dt $

which is easily integrated with Simpson's rule.  Hopefully this puts you 
on track for the others.  If not let me know.




-- 
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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