Re: Problem using Solve or Nsolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg124763] Re: Problem using Solve or Nsolve*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sat, 4 Feb 2012 06:32:40 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 2/3/12 at 2:10 AM, tototo at yopmail.com (droopy) wrote: >I am a new user of mathematica and i am trying to find the upper >limit of an integrate such as it is equal to a certain value. >Therefore, for the moment i did : f = (4^x)*E^-4/Gamma[x + 1]; >Reduce[{Integrate[f, {x, 0, A}] == 0.5}, {A}] >But it doesn't work, I did the same thing with Solve : >Solve[Integrate[f, {x, 0, A}] == 0.5, A] but it doesn't work. >The only way that i found to obtain a solution was with >FindRoot[Integrate[f, {x, 0, A}] == 0.5, {A, 2}] Using FindRoot is appropriate. NSolve, Solve and Reduce are not intended to handle this type of problem But there are a few things you should change. Don't use single upper case letters as variables. This ensures you will not have conflicts with built-in symbols. In this particular case, you didn't encounter a problem since there (currently) is no built-in symbol A. But if you get in the habit of using single upper case letters as variables, you will encounter problems eventually. Best to not do this. Using Integrate here is inefficient. This will cause Mathematica to try and find a symbolic solution to the integral for every time FindRoot supplies a new guess for the upper limit. That is you have Mathematica repeatedly trying to do something it cannot do. The way to set this up is to define a helper function: g[y_?NumericQ] := NIntegrate[f, {x, 0, y}] The test ?NumericQ and usage of SetDelayed (:=) ensures Mathematica will not attempt to evaluate g until a numeric value is supplied to g. Compare: In[10]:= Timing[FindRoot[g[x] - .5, {x, 2}]] Out[10]= {0.069981,{x->3.86298}} In[11]:= ClearSystemCache[]; Timing[FindRoot[Integrate[f, {x, 0, a}] - .5, {a, 2}]] Out[11]= {16.6628,{a->3.86298}} Both answers are the same but using Mathematica takes more than 200 times as long to get the answer when using Integrate instead of NIntegrate.