Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Determine the coefficients

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...

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Determine the coefficients

Interesting

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Determine the coefficients

I have noticed is that when a problem is thorny using classical methods

True but Niharika's question was not that thorny

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Determine the coefficients

Please check your signature at B and you will have my answer.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.