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Re: Integration of exp(az)*sigma(tto)*dz ??
Posted:
Dec 6, 1996 1:03 PM


In article <57jp6o$d42@brachio.zrz.TUBerlin.DE>, esfahani@mikro.ee.tuberlin.de (Farzad Esfahani) writes: > > > Hello you all, > Altough this may not be the right newsgroup I'll send to this group too > perhaps someone can help me. > I have to solve the following integration, who can help me or give me > some hints? > > I(t) = > A * Integral(from z=zo until oo) exp(a*z) * sigma(t  to) dz > > Where: > zo is the lower and oo (infinite) is the upper integral limit > A, zo and a are constants > to = (z  zo)^2 / D, with D as a constant > sigma is a step function and is defined: sigma = 0 for t<to > sigma = 1 for t>=to > > > My actual problem is to find a way to integrate the step function sigma. > Is there any possiblities to approximate it to a mathematical function. > Or is there any rule for its integration that I am not aware of it. > I have already looked in some Math books but I didn't find it. > > > PS.: Please send me your responses also via email, since I don't read this > newsgroup everyday. > > > Thanks in advance > > Farzad > If I understand your notation correctly, your integral reduces to
I(t) = A * (exp(a*(z0+sqrt(tD)))exp(az0)) for t>=0 and I(t)=0 otherwise since tt0<0 if (zz0)^2/D>t, i.e. z>z0+sqrt(tD) and sigma(u)=0 for u<0 and 1 otherwise. right? peter



