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Student Support Forum: 'Error in definite integral involving complete elliptic integrals' topicStudent Support Forum > General > "Error in definite integral involving complete elliptic integrals"

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Nicola Toschi
03/14/99 6:51pm

I have previously written (thanks to Tom Zeller for replying) with a problem with integration of functions like:

Integrate[r0*Cos[t]/Sqrt[z0^2 + (x0 - r0 Cos[t])^2 + (y0 - r0 * Sin[t])^2],{t,2,Pi}]

The result of the above is 0, which is not correct as can be seen e.g. with NIntegrate by setting any numerical values for the parameters. No warning message is generated. Plotting the indefinite integral

Integrate[r0*Cos[t]/Sqrt[z0^2 + (x0 - r0 Cos[t])^2 + (y0 - r0 * Sin[t])^2],t]

Plot[%, {t,0,2Pi}]

reveals a discontinuity in the indefinite integral (which uses EllipticF) and which is probably the (unrecognised) source of error. Is there any way I can get around this? It is necessary since using NIntegrate for every single (x0,y0,z0) is not really viable in terms of computer time. Thanks


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