Re: Help Improving this integral calculation / solution
- To: mathgroup at smc.vnet.net
- Subject: [mg108090] Re: [mg108044] Help Improving this integral calculation / solution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 8 Mar 2010 06:12:54 -0500 (EST)
- Reply-to: hanlonr at cox.net
d = 7/10; v = 5/100; a = 1/10; nk = (a + (1 - a) k v t)/(d + a + (1 - a) k v t) // Simplify (9*k*t + 20)/(9*k*t + 160) pg[k_] = Exp[1 - k]; gavg = Integrate[k pg[k], {k, 1, Infinity}] 2 result = 1/gavg Integrate[nk k pg[k], {k, 1, Infinity}, Assumptions -> 0 < t < 1] (9*t*(9*t - 70) - 11200* E^(160/(9*t) + 1)*ExpIntegralEi[ -1 - 160/(9*t)])/(81*t^2) test = FullSimplify[result] -((11200*E^(160/(9*t) + 1)* ExpIntegralEi[-1 - 160/(9*t)])/ (81*t^2)) - 70/(9*t) + 1 root = FindRoot[test == t, {t, .1}] {t -> 0.1420452943881465} Plot[{t, test}, {t, 0, .3}, Epilog -> {Red, AbsolutePointSize[4], Point[{t, t} /. root]}] test - t /. root -4.973799150320701*^-14 Bob Hanlon ---- DOD <dcodea at gmail.com> wrote: ============= I have an integral I need to calculate, with one variable left symbolic, and then use the result to find a numerical solution to an equation, and the result of the integration is not giving me what I need: ------ d = .7; v = .05; a = .1; nk = (a + (1 - a) k v t)/(d + a + (1 - a) k v t); pg[k_] = Exp[1-k]; gavg = Integrate[k pg[k], {k, 1, \[Infinity]}]; (* This is just 2 *) result = 1/gavg Integrate[nk k pg[k], {k, 1, \[Infinity]}, Assumptions -> 0 < t < 1]; test = FullSimplify[result] FindRoot[test == t, {t, .1}] ----- This code always gives up and stays at the initial guess. So, I look at the result of the integration, "result" (or it's simplified version, test2) and calculated it for various values of t, and it is always zero. ---- test/.t->{.1,.2,.3} ---- Output:{3.36999*10^66, 0., 0.} ----- So that's a problem. If I set t=.3, say, and the beginning, and calculate the integral, I get 0.160047, which is clearly not zero. ----- d = .7; v = .05; a = .1; t = .3; nk = (a + (1 - a) k v t)/(d + a + (1 - a) k v t); pg[k_] = Exp[1 - k]; gavg =Integrate[k pg[k], {k, 1, \[Infinity]}];(*This is just 2*) result = 1/gavg Integrate[nk k pg[k], {k, 1, \[Infinity]}] ---- Output=0.160047 ----- So there is a problem in the Integrate step. So I want to find a point where the output of that integral (result), as a function of t, satisfies result=t. Is there anyway to do this using built-in functions?