[pstricks] info about \psCumIntegral

[Carlo Alberini]

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}
> 
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