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

```

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