Re: Problem with integration
- To: mathgroup at smc.vnet.net
- Subject: [mg123710] Re: Problem with integration
- From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
- Date: Fri, 16 Dec 2011 05:48:13 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jccgt4$mlv$1@smc.vnet.net>
On Thu, 15 Dec 2011 10:07:32 -0000, Mehdi Mortazawi <mehdimortazawi at gmail.com> wrote: > Hi, > I was curious if there is difference between online Mathematica and > the one I have installed on my MAC(Mathematica version: 8.0.4.0). > The question rises from the problem that I am facing with numerical > integration. I want to integrate the following equation: > > NIntegrate[e^(-x) ((1 + 2 x)/(1)) (BesselK[0, 2 Sqrt[x] Sqrt[1+x]] > +BesselK[2, 2 Sqrt[x] Sqrt[1 + x]]) + (4 x^2 +2 x-1)*BesselK[1, 2 > Sqrt[x] Sqrt[1+x]]*e^(-x)/((1)Sqrt[x] Sqrt[1 + x]),{x,0,1}] > > When I type the equation on my computer, I receive the following > message: > " ...has evaluated to non-numerical values for all sampling points in > the region with boundaries {{0,1}" > but the online version gives the following answer which is the value I > am expecting: > > http://www.wolframalpha.com/input/?i=NIntegrate[e^%28-x%29+%28%281+%2B+2+x%29%2F%281%29%29+%28BesselK[0%2C+2+Sqrt[x]+Sqrt[1%2Bx]]%2BBesselK[2%2C+2+Sqrt[x]+Sqrt[1+%2B+x]]%29+%2B+%284+x^2+%2B2+x-1%29*BesselK[1%2C+2+Sqrt[x]+Sqrt[1%2Bx]]*e^%28-x%29%2F%28%281%29Sqrt[x]+Sqrt[1+%2B+x]%29%2C{x%2C0%2C1}] > The difference in this case is that Wolfram Alpha is more lenient with respect to what it accepts as input. The reason Mathematica doesn't give an answer is because e is not defined. But if you define it, say as \[ExponentialE], then you will get: e = \[ExponentialE]; NIntegrate[ e^(-x) ((1 + 2 x)/(1)) ( BesselK[0, 2 Sqrt[x] Sqrt[1 + x]] + BesselK[2, 2 Sqrt[x] Sqrt[1 + x]] ) + (4 x^2 + 2 x - 1)*BesselK[1, 2 Sqrt[x] Sqrt[1 + x]]*e^(-x)/((1) Sqrt[x] Sqrt[1 + x]), {x, 0, 1} ] 1.245 Wolfram Alpha gives this answer after having guessed that the intended value of e is \[ExponentialE]. But if you want the same result from Mathematica, you have to be specific about the values involved.