Funktionen mit Integralen definieren

Torsten shared this question 9 months ago
Answered

Ich würde gerne Funktionen mit Hilfe von Integralen definieren.


Konkretes Beispiel: Für eine gegebene Funktion U möchte ich eine Funktion V definieren mit


V(x)=integral_0^1 (1 / (U(y) - x) ) dy


Ist soetwas mit Geogebra möglich?


Ich weiß, dass ich mit den Funktionalitäten Animation und Spur zeichnen den Graphen von V zeichnen lassen kann. Das hilft mir jedoch in sofern nicht weiter, dass ich mit der Funktion V anschließend noch weiter arbeiten möchte - also ableiten, invertieren etc.


Wenn es hierfür eine Lösung gäbe, so wäre mir sehr geholfen.

Dank und Gruß

Torsten

Comments (5)

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It's a bit tricky, but you can do it like this:


https://www.geogebra.org/m/nrxmfnmf

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Thank you for your advice. It helped me a lot. Is there a way how to apply the usual analysis commands to the resulting function? I am thinking of the determination of zeros, extremals, and derivatives.

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Thank you @Michael Borcherds!!!!

This is the answer to a part of my problem in:

https://help.geogebra.org/topic/bug-in-the-command-curve-that-uses-the-command-integral_1

f(x) = cos(π x² / 2); Integral(f, 0, u)), u, 0, 5) →F(x) = DataFunction[x]

h1 = Curve((u, Integral(f, 0, u)), u, 0, 5)-->

h1 = Curve((u, F(u)), u, 0, 5) work!

in the attached file.

And for 2-dimensional cases .... F(x,y)

Surface(u, v, Integral(cos( u² +v^2 ),0, 3), u, -5, 5, v, 0, 14)

It is very useful option. For example, it is implemented in

http://mathworld.wolfram.co...

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I am thinking of the determination of zeros, extremals, and derivatives.


You can try but I don't think they will work well (if you zoom the function up it is very "jagged")

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Unfortunately, these analysis tools do not work.


Meanwhile, however, a more important problem has arisen. The functions defined using the locus command appear to require a great deal of processor power.


The creation of the first function I (x) = integral U (x, y) dy works perfectly. In the second function J (x) = integral V (x, I (y)) dy, however, geogebra becomes extremely slow, no longer responding to further inputs or crashes completely.


I've been trying to reduce the needed processing power by expanding the increment of the underlying slider. Unfortunately, that did not lead to the relief expected.


For any indication of how to improve the stability of the application, I would be grateful.


Thanks for your advices

Torsten

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