# Get same numerical and analytical integral's results?

Posted 1 month ago
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 Good morning-Afternoon. I was recently programing an integral and decided to check how it would work compared to a numerical aproximation. I used Simpson and trapezoid rules. However, my results are several orders of magnitude different. I have attached my code.Can someone please give me some hindsight on what I am doing wrong?Thank you very much. Attachments:
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Posted 1 month ago
 There are a number of ways to improve on this. Most important error is to not multiply trapezoid heights by step length. The value below is pretty good for an approximation. step*(Total[Map[gausiana, N[PuntosEnsayo[[2 ;; -2]]]]] + 1/2 (gausiana[PuntosEnsayo[[1]]] + gausiana[PuntosEnsayo[[-1]]])) (* Out[192]= 0.0000718038661611 *) 
Posted 1 month ago
 I see. Thank you bery much for the information. I am afraid I am not fluent enough in mathematica to propperly understand your proposed aproximation, but I will try to comprehend it.
 Jaime,your approach is basically correct. But you give the number of a point to the gaussian and not the x-value, which is in fact PuntosEnsayo[[i]] and not i. i is the number of your x-value. And you start with i =0, which is problematic for Tables.Try in your code For[i = 1, i < numero, i++, valorNumerico = valorNumerico + step ((1/2)*(gausiana[PuntosEnsayo[[i]]] + gausiana[PuntosEnsayo[[i + 1]]]))]; For[i = 1, i < numero, i++, valorNumericoSimpson = valorNumericoSimpson + step (1/6)*(gausiana[PuntosEnsayo[[i]]] + gausiana[PuntosEnsayo[[i + 1]]] + 4*gausiana[PuntosEnsayoMedios[[i]]])]; valorNumerico valorNumericoSimpson Daniel's approach is Mathematica-like (avoid Do's, For's and so on if possible) and elegant.He applies gausiana to each x-value, meaning each value in PuntosEnsayo. This is done with the Map-command. Then he adds all these values ( Total ) and finally multiplies with your step-width. You can achieve this as well with step*Total[gausiana /@ PuntosEnsayo] neglecting the contributions at the ends of the interval Attachments: