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 05-03-2011, 11:09 AM #11 Guru     Join Date: Jan 2008 Location: U.S. Posts: 7,841 Re: Is this computer learning? Eh? The indefinite integral to sin(x)/x is Si(x) + C... __________________
 05-03-2011, 11:10 AM #12 BSOD   Join Date: Dec 2010 Posts: 582 Re: Is this computer learning? You're only cheating your self. God I sound like my German teacher. __________________
05-04-2011, 01:37 PM   #13
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Join Date: Jun 2010
Posts: 193
Re: Is this computer learning?

Quote:
 Originally Posted by j03 Yeah, that's for the definate integral - as in a numerical answer. It's impossible to get a finite algebraic answer to the integral of sin(x)/x
In a manner of speaking, you can't get a finite answer to sin(x) or cos (x) either.

Here's what I'm getting at. Sin(x) + C is the integral of cos(x). Now sin(x) ranges from -1 to +1 which includes an infinity of irrational numbers (e.g. the square root of 2 divided by 2). When you express an irrational number as a decimal, then it's not closed as it keeps going on forever so expressions such as sin(x) and cos(x) I don't regard as being truly closed form expressions (which makes me an intuitionist to an extent just like Kronecker and Brouwer were).

05-04-2011, 06:17 PM   #14
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Join Date: Jan 2008
Location: U.S.
Posts: 7,841
Re: Is this computer learning?

Quote:
 Originally Posted by Comp Explorer In a manner of speaking, you can't get a finite answer to sin(x) or cos (x) either. Here's what I'm getting at. Sin(x) + C is the integral of cos(x). Now sin(x) ranges from -1 to +1 which includes an infinity of irrational numbers (e.g. the square root of 2 divided by 2). When you express an irrational number as a decimal, then it's not closed as it keeps going on forever so expressions such as sin(x) and cos(x) I don't regard as being truly closed form expressions (which makes me an intuitionist to an extent just like Kronecker and Brouwer were).
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