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sum of integrals over patial intervals != integral over whole interval
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71719] sum of integrals over patial intervals != integral over whole interval
*From*: Peter Pein <petsie at dordos.net>
*Date*: Mon, 27 Nov 2006 04:04:49 -0500 (EST)
Dear group,
I wanted Mathematica to show, that for f[x_]:=Log[Sin[x]^2]Tan[x],
Integrate[f[x],{x,0,Pi}]==0, because f[x]+f[Pi-x]==0.
Mathematica says Integrate[f[x],{x,0,Pi}] does not converge, but
Integrate[f[x],{x,0,Pi/2}] and Integrate[f[x],{x,Pi/2,Pi}] evaluate to
-Pi^2/12 resp. P^2/12 and the sum is zero. The more general integral
Integrate[f[x],{x,0,z},Assumptions->Pi/2<z<=Pi] evaluates explicitly (?).
What did I do wrong?
http://people.freenet.de/Peter_Berlin/Mathe/komisch.nb
TIA,
Peter
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