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MathGroup Archive 2007

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Boole does not work with symbolic limits in Integrate ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73102] Boole does not work with symbolic limits in Integrate ?
  • From: Mitch Murphy <mitch at mix5.com>
  • Date: Sat, 3 Feb 2007 04:16:07 -0500 (EST)

hey hey

use of the boole indicator function inside integrate only works for  
numerical arguments, symbolic limits of integration just returns the  
unevaluated integral.

simple example ...

	Integrate[2 u Boole[a < u], {u, 0, x}]
	
	out[] = Integrate[2 u Boole[a < u], {u, 0, x}]

i would expect ...

	Integrate[2 u , {u, a, x}]

	out[] = x^2 - a^2

but it does work with numerical limits of integration ...

	Integrate[2 u Boole[a < u], {u, 0, 2}]
	
	out[] = Piecewise[{{4, a <= 0}, {4 - a^2, 0 < a < 2 }]


anybody know a trick to make this work ? i've tried a bunch of  
variations using evaluate[], logicalexpand[], piecewiseexpand[],  
assumptions->x Reals, ..., but nothing works.

cheers,
Mitch


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