Integration and Differentiation
Just a quick question to ask: Is it possible to write a program to find the integration and differentiation of a given function? Say f(x) = cos 3x + e^x;
Please if yes,how do i go about it? If no,then I'll just keep thinking.
Please if yes,how do i go about it? If no,then I'll just keep thinking.
think in the factorial way
for eg x^2 then integrating that will give x^3/3 . I will also try too.
for eg x^2 then integrating that will give x^3/3 . I will also try too.
If you know the function in advance, it's relatively easy to come up with a numerical answer.
If the user can type in whatever equation they like, it becomes harder (see "equation parsing").
If the user can type in whatever equation they like, it becomes harder (see "equation parsing").
I've written a program which can differentiate an arbitrary function symbolically. Symbolic integration is way more difficult (but not impossible).
For differentation probably the most difficult part is parsing the function into someshort of syntax tree. After parsing it is a very straightforward and trivial algorithm (which will result in a very long function, that can be simplified either by hand or algorithmically to the common, shorter form).
About symbolic integration :
http://en.wikipedia.org/wiki/Symbolic_integration
Numeric integration is relatively easy.
For differentation probably the most difficult part is parsing the function into someshort of syntax tree. After parsing it is a very straightforward and trivial algorithm (which will result in a very long function, that can be simplified either by hand or algorithmically to the common, shorter form).
About symbolic integration :
http://en.wikipedia.org/wiki/Symbolic_integration
Numeric integration is relatively easy.
Yes, it is possible. Mathematika, MATLab, Derive and what else is out there can do that. I would start out with the simple ones and a "look-up-table".
Since ln(x) integrated is 1/x that one is not so difficult. Same with sin(x) or cos(x) etc. The same is for the differentiation. cos(x) is - sin(x) and so forth.
Since ln(x) integrated is 1/x that one is not so difficult. Same with sin(x) or cos(x) etc. The same is for the differentiation. cos(x) is - sin(x) and so forth.
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