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MathGroup Archive 2002

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Simplified Integration Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35564] Simplified Integration Problem
  • From: Arnold Gregory Civ AFRL/SNAT <Gregory.Arnold at wpafb.af.mil>
  • Date: Fri, 19 Jul 2002 06:08:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Here's a slightly simplified version of the integration problem I presented the other day:

int=Integrate[UnitStep[1 - t^2 - c^2*(-4*t + 8*t^3)^2], {t, -1, 1}];
int /. c->0    Result:2
int /. c->0.   Result:0.
int /. c->3    Result:2
int /. c->3.   Result:0.28817

In fact, "int /. c-> any rational" always yields 2!!!

NIntegrate gets the right answers:
NIntegrate[UnitStep[1 - t^2 - 0^2*(-4*t + 8*t^3)^2], {t, -1, 1},
MinRecursion->5,MaxRecursion->30]      Result: 2

NIntegrate[UnitStep[1 - t^2 - 2^2*(-4*t + 8*t^3)^2], {t, -1, 1},
MinRecursion->5,MaxRecursion->30]      Result: 0.28817

Plot[int,{c,-5,5}]  also gets the right results.

Any help or insight into why Integrate isn't working would be greatly appreciated!

Greg




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