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MathGroup Archive 2002

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RE: Why can't Mathematica do this simple integral ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36819] RE: [mg36808] Why can't Mathematica do this simple integral ?
  • From: "DrBob" <drbob at bigfoot.com>
  • Date: Fri, 27 Sep 2002 04:15:19 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

You would need to make assumptions about y, and you can't.  The function
and the limits have to take care of that, and when you try to do that,
you end up with an expression that has different antiderivatives on
different regions, for different values of x.  So, you have to break it
up.  The assumption x > 0 implies that x is real, so Im[x]==0 is
unnecessary.

one = Integrate[Cosh[2 (y - x)] 
      2 y, {y, Min[x, 1/2], 1/2}, Assumptions -> {x > 0}];
two = Integrate[Cosh[2 (x - y)] 2 
      y, {y, 0, Min[x, 1/2]}, Assumptions -> {x > 0}];
one + two // FullSimplify
Plot[{one, two, one + two}, {x, 0, 1/2}];

 (1/4)*E^(-1 - 2*x)*(E + (-2 + E)*E^(4*x))

Bobby Treat

-----Original Message-----
From: Madhusudan Singh [mailto:spammers-go-here at yahoo.com] 
To: mathgroup at smc.vnet.net
Subject: [mg36819] [mg36808] Why can't Mathematica do this simple integral ?

Hi
        I have been trying to integrate the following :

        Integrate[Cosh[2 Abs[x-y]] 2 y, {y,0,1/2},
  Assumptions->{Im[x]==0,x>0}]

        However, Mathematica chokes and simply returns the integral as
it is. However, if I
 split up the integral into two portions, it quickly gives me an answer
for the parts. Is
 there something implicit that I am missing in the Assumptions ?

Thanks,

MS.

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