Hello Andrey,

Please look at the picture:

I can not understand this. There must be something in the definite integral realization in SMath.
1. The function defined F(x) as definite integral with variable limit x can be defined
2. Calling this function will give the result
3. Plotting of this function is not possible???
4. Solve, f.e. with this function will not give the result???

Could you give me some hints what is this about?

Regards,
Radovan

Hi Radovan,

I think the problem you have found is issued in a topic before (see: http://en.smath.info/for...lt.aspx?g=posts&t=85)
The definite integral is only nummerically implemented so far (at least it was the days when the other post was written), therefore it is impossible to plot the solution of a definite integral. Of course there is no problem with numerically solving it.
If you try to symbolically solve your integral, there will be an error (limits must be real).

So currently it is simply not possible to symbolically integrate.

But why the plot is wrong, Andrey has to answer.

Ciao Jakob

Here is the example of Definite Integral plotting by points:

Thanks Andrey,

I understood that. I intentionally put this, because many times this happened to my students in Mathcad. I was expecting that some error should be issued in SMath with this expression when, say, plotting it.
F(x)←int(x^3+10;x;0;x)
But, it worked and I was puzzled about it?. In the first place, how this could be plotted (wrongly) considering the rules about plotting and definite integral as numerically solved?
This might cause problems in Mathcad in spite of that it could solve it analitically, until you use the correct expression (the limit variable should not be the same as the variable in the primitive function) say
F(x)←int(t^3+10;t;0;x)

Your example about plotting the function with definite integrals is quite understandable and this plot is right, but please take a look at your (correct) plot and the one I mentioned incorrect (the blue line represents F(x)). What is this about?

Regards,
Radovan

Oh damn!! Sorry RADOVAN!!! It was just a typo error, I swear!!
Jakob

If this is the case i.e. Newton like procedure with analitical derivatives, it is quite understandable then.

Thanks Jakob,
Radovan

omorr, thanks for the example above. I think jakobg talk about typo in the url. Here is a right one: http://en.smath.info/for...lt.aspx?g=posts&t=85

Hi,

well, actually my typo was something different, but if nobody "found" it, I am not going to mention it here.
An interesting topic is, I have copied the url from my adress bar and I too get the error access denied.
Thanks Andrey for the link, this was the post I was talking about.

Ciao Jakob

Hello Stephan,

It was mentioned in some other posts (for example "int" does not like "if"?) I suppose this is due to the internal SMath
numerical integration. If you want to integrate a discontineous function try something like this:
f(x)←(x<5)*3+(x≥5)*5
int(f(x);x;-4;8)=42,04
(Pay attention on the numerical error, the result is 42 actually. Try to avoid using this or see the example on Wiki)

Put it on some free file hosting and make a link to it via "Create link" tool when posting.

Regards,
Radovan

Edited by user 20 February 2010 01:50:06(UTC)  | Reason: Not specified

Hello Radovan,

thank you very much for the quick reply and the helpful links.
I will try to split my definite integral into sections where my function is continous.

Regards
Stephan

Also thanks to Greg for the hint with the wiki.