numerical integration __ integral limits being variables

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Meva
Meva 2015-4-5
编辑： Meva 2015-4-5
Hello, I want to numerically integrate functions whose upper limits x, lower limits 0. Say;
int_0^x f(x) dx
Which method should I use. trapz, simpson, or omething else and which command ?
I mean can you send a simple example of doing this please? Thanks

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Roger Stafford
Roger Stafford 2015-4-5
There are a number of ways you can proceed. One way is to use 'int' with a variable upper limit. See:
http://www.mathworks.com/help/symbolic/int.html
If that does not succeed (which often happens) you can do numerical integration using the 'cumtrapz' function which also allows you to have a variable, though discrete, upper limit. See
http://www.mathworks.com/help/matlab/ref/cumtrapz.html
Finally, there are several functions in the File Exchange which are numerical but have higher precision. I wrote one of these. It is located at:
http://www.mathworks.com/matlabcentral/fileexchange/19152-cumulative-cubic-integration

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Star Strider
Star Strider 2015-4-5
If you are numerically integrating functions, use integral (or quad and its friends if you don’t have integral). You will obviously have to define what value ‘x’ is to do a numerical integration.
If you want to do a symbolic integration (and your function is integrable), use the Symbolic Math Toolbox int function.
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Star Strider
Star Strider 2015-4-5
You can use cumtrapz with data returned by your function, but not with your function itself. If you want to use a function, you have to use integral or quad, as I wrote before.
Meva
Meva 2015-4-5
编辑：Meva 2015-4-5
what do you mean by that Can you explain more please?
I have used like:
x=linspace(0,1,0.01)
cumtrapz(x, 4*(x-0.5))
Can't I use it? It is supposed to be
int_0^x 4*(x-0.5) dx

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