[pstricks] info about \psCumIntegral
Carlo Alberini
carloalbe1 at yahoo.it
Thu Dec 13 20:27:24 CET 2018
Dear Alexander,
it is simply perfect!
I read the code, and I understood almost everything. Now I will try to modify it in order to obtain other integral function like in the sample.
Thank you so much!
Best regards
Carlo
> Il giorno 13 dic 2018, alle ore 18:12, Alexander Grahn <A.Grahn at hzdr.de> ha scritto:
>
> On Thu, Dec 13, 2018 at 02:57:12PM +0100, Carlo Alberini wrote:
>> Dear Alexander,
>> thank you for your mail; I think about a function like:
>>
>> $\int_{2x+3}^{\frac{1}{x+1}}f(t)dt$, with some f(t) as you like.
>>
>> It would be fantastic if I could have the plot af such a function… written with the “algebraic” option (easy and fast …)
>>
>> Thank you
>> Carlo
>>
>>> Il giorno 13 dic 2018, alle ore 14:47, Alexander Grahn <A.Grahn at hzdr.de> ha scritto:
>>>
>>> Dear Carlo,
>>>
>>> On Thu, Dec 13, 2018 at 01:25:56PM +0100, Carlo Alberini wrote:
>>>> Dear list,
>>>> I write this message after reading the pst-func manual. I have found very interesting the command \psCumIntegral and I have two questions about it:
>>>>
>>>> - the command works only with the integration interval from 0 to x, or si it possible to put - as integration interval - also two functions like f(x) and g(x)? ... in order to have the plot of an integral function like $F(x)=\int_{f(x)}^{g(x)}f(t)dt$ ...?
>>>>
>>>> and
>>>>
>>>> - is it possible to write, in such a way, the function under the integral operator with the option “algebraic”, or not? ... like this ...
>>>>
>>>> \psCumIntegral[algebraic,plotpoints=1000,Simpson=10,linecolor=blue]{1}{9}{ln(x)/(1+x^3)}
>>>>
>>>> Thank you so much for your help and your tips!
>>>>
>>>> Best regards
>>>> Carlo
>>>
>>> could you please specify f(x) and g(x)?
>>>
>>> Alexander
>
> Here, \pstODEsolve from package pst-ode is (ab)used for integrating ln(t)/(1+t^3)
> between g(x)=2x+3 and h(x)=1/(x+1).
>
> Everything input in algebraic notation (infix notation). Some Postscript
> required for assembling result list `result' to be plotted with
> \listplot from pst-plot.
>
> Hope this is what you expect.
>
> Alexander
>
> \documentclass[a5paper]{article}
>
> \usepackage{pst-ode,pst-plot}
>
> \begin{document}
>
> \pstVerb{/result {} def} %initialise empty result list
> \multido{\nX=1.00+0.01}{801}{% 801 plotpoints for x=1.0, 1.01, ..., 9.0
> % one call of \pstODEsolve returns integral = [g(x) 0 h(x) F(h(x))] --> two output points
> %
> % format for `integral'----v two output points---v v---initial value at g(x)
> \pstODEsolve[algebraicAll,silent]{integral}{t | y[0]}{2*\nX+3}{1/(\nX+1)}{2}{0.0}{ln(t)/(1+t^3)}
> % integration interval from g(x)----^ to ^----h(x)
> %
> % append [x F(h(x))] to results list
> \pstVerb{/result [result \nX\space integral exch pop exch pop exch pop] cvx def}
> %
> %print to stdout
> \pstVerb{[\nX\space integral exch pop exch pop exch pop] ==}
> }
>
> \begin{equation}
> f:x \mapsto \int_{2x+3}^{1/(x+1)} \frac{\ln(t)}{1+t^3}\, \textrm{d}t
> \end{equation}
>
> %plot result
> \psset{xunit=0.5,yunit=500}
> \begin{center}
> \begin{pspicture}(-3,-0.006)(10,0)
> \psaxes[Dx=1,Dy=0.001](0,0)(0,-0.006)(10,0)
> \listplot[linecolor=red]{result}
> \end{pspicture}
> \end{center}
> \end{document}
>
> _______________________________________________
> PSTricks mailing list
> PSTricks at tug.org <mailto:PSTricks at tug.org>
> http://tug.org/mailman/listinfo/pstricks <http://tug.org/mailman/listinfo/pstricks>
> archive: http://www.tug.org/pipermail/pstricks/ <http://www.tug.org/pipermail/pstricks/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://tug.org/pipermail/pstricks/attachments/20181213/e9940ddf/attachment-0001.html>
More information about the PSTricks
mailing list