<![CDATA[Math Is Fun Forum / Determine the coefficients]]> 2015-08-29T19:06:03Z FluxBB http://www.mathisfunforum.com/viewtopic.php?id=22482 <![CDATA[Re: Determine the coefficients]]> Please check your signature at B and you will have my answer.

]]>
http://www.mathisfunforum.com/profile.php?id=33790 2015-08-29T19:06:03Z http://www.mathisfunforum.com/viewtopic.php?pid=366504#p366504
<![CDATA[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

]]>
http://www.mathisfunforum.com/profile.php?id=95904 2015-08-29T15:45:23Z http://www.mathisfunforum.com/viewtopic.php?pid=366502#p366502
<![CDATA[Re: Determine the coefficients]]> Interesting

]]>
http://www.mathisfunforum.com/profile.php?id=95904 2015-08-29T15:42:25Z http://www.mathisfunforum.com/viewtopic.php?pid=366501#p366501
<![CDATA[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...

]]>
http://www.mathisfunforum.com/profile.php?id=33790 2015-08-29T08:26:56Z http://www.mathisfunforum.com/viewtopic.php?pid=366487#p366487