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**bobbym**- Replies: 0

This problem appears in another thread and similar ones pop up on contest sites where they are considered tough. One of the oddities that I have noticed is that when a problem is thorny using classical methods it will often succumb to EM rather easily. This is certainly the case here.

Here is the problem:

and we are asked to solve for a,b,c,d,f.

Whatever those coefficients are they might just work for definite integrals too. This reduces the problem to solving a 6 x 6 simultaneous set of linear equations and to the numerical evaluation of 6 integrals. This of course is generally a trivial matter to almost all the software out there.

We obtain the six integrals using Gaussian or Romberg integration.

If we call the RHS of 1) g(x) we have:

We know from calculus that

We can now easily follow the pattern and generate the 6 simultaneous equations.

Solving for a,b,c,d,f we get:

a = -4

b = -12

c = -20

d = 0

f = 32

More to come...

Hi;

That is an acronym for Experimental Mathematics.

Hi;

Those are nice ideas, you are correct in trying to get them to answer the first question everyone has...what is this good for? Once that is out of the way, progress is possible.

Hi;

Yes, Pythagorean triples.

Did you draw a good diagram?