Re: Integration using mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg72640] Re: Integration using mathematica*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sat, 13 Jan 2007 04:30:02 -0500 (EST)*References*: <eo7mt2$1ps$1@smc.vnet.net>

First things first! In order to use Mathematica you should first learn the Basic Syntax of it! Here is a good place to start: Copy/paste the following command in a notebook and execute it! FrontEndExecute[{HelpBrowserLookup["MainBook", "T.0"]}] You are right for example about the first letter being capitalized; but on the other hand arguments of functions must be enclosed on square brackets. Apart from this your input misses some parentheses and I was not able to figure out exactly your expression! Suppose I am right and I guess well, let f be the following expression f = 0.013*Exp[15.16*ArcTan[0.002*x]^2]*ArcTan[0.002*x]; One thing you should learn for your very begining in using Mathematica is not use inexact numbers for symbolic calculations like integration. You can consult the archives of this forum if you want more details about why. A quick way to convert your real numbers to exact Rational numbers is by using Rationalize. Then ff=Rationalize[f] (13*E^((379/25)*ArcTan[x/500]^2)*ArcTan[x/500])/1000 Let's try to integrate (indefinite integral) this exression w.r.t. x. We get Integrate[ff, x] (13*Integrate[E^((379/25)*ArcTan[x/500]^2)*ArcTan[x/500], x])/1000 Mathematica fails to return a analytical result. There are three alternative explanations: 1) There is not a closed form expression. Especially for indefinite integrals usually this is the case within Mathematica. 2) Mathematica does not know the integral. Seldom especially for indefinte integrals. 3) Mathematica "needs" a little help in order to determine the integral. Let know try definite integral of this expression. There are many occasions that there is not a closed form expression for an indefinite integral but there are closed form expressions for definite integrals. For example Integrate[BesselJ[0, x]/(1 + x^2), x] Integrate[BesselJ[0, x]/(1 + x^2), x] However, Integrate[BesselJ[0, x]/(1 + x^2), {x, 0, Infinity}] (1/2)*Pi*(BesselI[0, 1] - StruveL[0, 1]) Moreover, in definite integration you have also the numerical "way". A quick check of the last result: N[%] 0.8730842426508671 NIntegrate[BesselJ[0, x]/(1 + x^2), {x, 0, Infinity}, Method -> Oscillatory] 0.8730842426508675 So, let integrate definite ff, say between 0 and Pi. Before performing a definite integration (symbolic or numerical) always plot the integrand for possible singularities in the intagrtion range. Plot[(13*E^((379/25)*ArcTan[x/500]^2)*ArcTan[x/500])/1000, {x, 0, Pi}, PlotPoints -> 1000] The graph, show normal behavior of the integrand. Warning, howver, that the graph does not guarranty that! Anyway, Integrate[ff, {x, 0, Pi}] Integrate[(13*E^((379/25)*ArcTan[x/500]^2)*ArcTan[x/500])/1000, {x, 0, Pi}] Again no closed form result! Finally, NIntegrate[ff, {x, 0, Pi}] 0.00012834241443264268 I hope you will find my reply helfpful. Try to repost your message with correct syntax if my guess was not right! Regards Dimitris Negede wrote: > I have difficulty in integrating the following equation on Mathematica. > Does any one of you know how to do it on Mathematica? Any trick to > aply? or another software to use? Please help me. The function is as > follows: > > 0.013 *Exp [15.16(ArcTan(0.002 x)])^2 *(ArcTan(0.002 x) > > Thanks in advance