multiple solutions in schaum's outline

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gistick
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multiple solutions in schaum's outline

Postby gistick » Wed Jun 08, 2011 5:38 pm UTC

In Schaum's outline "Mathematical Handbook of Formulas and tables" in the chapter on indefinite integrals (chap 17 of the 1999 copyright version) once and a while two solutions are provided. For example in the section of "integrals involving sinax and cosax" on page 89, integral number 17.19.22 has two solutions. Am I correct to say these are two different solutions? Or are they solutions under different cases? It appears they are different (unless I am messing something up when I evaluate them...). Please clarify this for me if you can. Google books has a preview of the page in question http://books.google.com/books?id=jIMHMX ... &q&f=false.
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-tim Szczykutowicz
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www.quarkquark.com/electronman/

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Dopefish
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Re: multiple solutions in schaum's outline

Postby Dopefish » Wed Jun 08, 2011 5:53 pm UTC

At a glance, it looks like they're solutions for different cases (namely for r^2>p^2+q^2 and r^2<p^2+q^2). edit: Initially looked at a different example of something giving more than one solution , where p^2>q^2 or vice versa was what mattered.

I'm surprised they don't specify that somewhere though, as it may not always be obvious what the differing cases are, and whether q^2=p^2 requires a different formula entirely, or if one or both simplifies down to the same thing in that instance. edit: Your specific example does mention what to do in the case they're equal.
Last edited by Dopefish on Wed Jun 08, 2011 5:57 pm UTC, edited 2 times in total.

Hix
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Re: multiple solutions in schaum's outline

Postby Hix » Wed Jun 08, 2011 5:56 pm UTC

They are solutions in different cases, depending on the sign of the expression under the radical. One is for r^2 > p^2 + q^2, the other for r^2 < p^2 + q^2.

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gistick
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Re: multiple solutions in schaum's outline

Postby gistick » Wed Jun 08, 2011 6:03 pm UTC

I agree, that makes sense based on what I am playing with now. I numerically evaluated the integral for a few different cases and it agrees with what you guys are saying. This is what I had guessed was the case (no pun intended) but I wanted to see what some other people thought - it would be nice if Schaum's defined the cases. They must think if anyone wants to carry out such integrals they should know what they are doing... Thanks again.
-tim Szczykutowicz
maker of "Electron Man" webcomic
www.quarkquark.com/electronman/


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