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simple integrals give give difficult results
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Integrating the simple functions 1/x, 1/x², 1/x³ upwards from 1 give correct results for low values of the upper limit but with the upper limit in the order of 200 or higher the results are not what I would expect. Please see the attached worksheet. Is there a problem with the integral function or is there something I haven't grasped? H integral.sm (6kb) downloaded 11 time(s).Edited by user 12 August 2019 22:55:34(UTC)
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Hi. It's because the integral it's a numerical procedure, and maybe not a very robust one. So, like any numerical method, if it don't work, just use another. integral.sm (14kb) downloaded 10 time(s).Best regards. Alvaro.




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Hakelm, I opened your file and the results were correct. Therefore I believe that the parameter for the accuracy of the integrals in your SMath installation is not correctly set. Try to change Tools>Options>Calculation>Integral Accuracy For example, write 1000 However, Alvaro's considerations must be kept in mind sergio Edited by user 13 August 2019 12:53:24(UTC)
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Many thanks for two very good answers! Now I know that Smath doesn't know even the simplest of integrals but that approximation accuracy can be improved upon. Even if I understand my system doesn't (SMathStudioDesktop.0_99_7109.Mono on Ubuntu 16.04). It can't find the function Rkadapt. I guess that the RungeKutta functions are to be found i some plugin. Where can I find that? H




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Originally Posted by: hakelm I guess that the RungeKutta functions are to be found i some plugin. Where can I find that? ODE Solvers. 




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Originally Posted by: hakelm Is there a problem with the integral function or is there something I haven't grasped? The Simpson integrator ranges from exact to freak. In your examples, increase the integral accuracy from menu, options, calculations, integral accuracy [max 10000] Wise to sanity Wolfram Alpha cost is 0.00 $ integral.sm (47kb) downloaded 6 time(s).




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May I assume that the SMathintegral is made using Simpson's rule and that the integral accuracy [max 10000] is the number of steps taken by Simpson? H




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Originally Posted by: hakelm May I assume that the SMathintegral is made using Simpson's rule and that the integral accuracy [max 10000] is the number of steps taken by Simpson? Quite right: The Smath integrator is Simpson. Ranged accuracy [50 ... 10000]. Trivial cases are exact. Two more exact cases are know 1/x [ln(x), b_spline]. On long range of the variate 'x' the Simpson/Romberg kernel gives a much better result than simple Simpson. Carlos adaptive algorithm is fool proof all cases.You want these two proposed ... reply YES/NO. Jean




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