       Can Integrate[expr,{x,a,b}] give an incorrect result?

• To: mathgroup at smc.vnet.net
• Subject: [mg81827] Can Integrate[expr,{x,a,b}] give an incorrect result?
• From: "W. Craig Carter" <ccarter at mit.edu>
• Date: Thu, 4 Oct 2007 04:27:21 -0400 (EDT)

I believe I am getting an incorrect result from a definite
integration:

InputForm[integrand] is
(R*(R - rho*Cos[alpha - t]))/(3*(R^2 + rho^2 + (z - zeta)^2 - 2*R*rho*Cos[alpha - t])^3)

InputForm[assumptions] is
{R > 0, L > 0, rho > 0, Element[zeta, Reals], Element[z, Reals], alpha > 0}

Integrate[integrand,{t,0,2Pi},Assumptions->assumptions]
returns 0

But compare this to:
(visually integrate...)
Plot[integrand/.{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z -> 1.2},{t,0,2 Pi},PlotRange->All]

(numerically integrate...)
Plot[NIntegrate[integrand/.{{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z -> 1.2},{t,0,tau}],{tau,0,2Pi}, PlotRange->All]

Something isn't adding up??

Thanks, WCC

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