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Integrate vs Nintegrate for impulsive functions

• To: mathgroup at smc.vnet.net
• Subject: [mg61690] Integrate vs Nintegrate for impulsive functions
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Wed, 26 Oct 2005 01:01:44 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi Folks


I have an expression resulting from a fourier series (for a 1D wave 
equation for a string) (fourier coeffficient) of the form

h[x_]=(-0.24982234345508192 - 0.0429732983215806*I)*
 Sin[(3.1734427242687215 + 0.3295480781081674*I)*x]*
 (Cosh[1000.*(-0.4 + x)^2] - Sinh[1000.*(-0.4 + x)^2])

I try to integrate this on the domain x(0,1) to get the fourier 
coefficient. I get some results that I need help explaining


Integrate[h[x],{x,0,1}]

 >>0+0 *I

NIntegrate[h[x],{x,0,1}]

 >>-0.0133612 - 0.00285551 \[ImaginaryI]

Is the result from NIntegrate valid

The initial condition is essentially a smoothed delta function at x=0.4

gxx[x_]=E^(-1000.*(-0.4 + x)^2)

Please advise


Regards


Pratik .

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134

• Follow-Ups:
  • Re: Integrate vs Nintegrate for impulsive functions
    • From: Chris Chiasson <chris.chiasson@gmail.com>