How to use trapz or cumtrapz function to integrate a function from -infinity to t?

clc;

close all;

clear all;

p = 2;

num_gamma= gamma(3/p);

den_gamma= gamma(1/p);

global a;

a=(p/2)*(((num_gamma)^(1/2))/((den_gamma)^(3/2)))

global b;

b=(num_gamma/den_gamma)^(p/2)

tau = -100:0.01:100;

for t = 1:length(tau)

      f(t)=a*(exp(-b*((abs(tau(t)))*p)));

**  F=cumtrapz(tau,f(t));**

      g=(f.^2)./(1-F);

end

plot(g,tau)

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I NEED TO INTEGRATE THE FUNCTION 'f' FROM MINUS INFINITY TO tau, HOW CAN I DO THAT?

Answer 1

[John D'Errico]

Please don't ask the same question over and over again. I'll answer this only because it is SLIGHTLY different from your other nearly identical question.

trapz and cumtrapz cannot solve problems on an infinite domain. Well, they can, but it will take infinitely long, and require an infinitely large computer. Infinity is a big place.

Of course, you can try a transformation of your function, to convert the infinite domain into a finite one. Not all transformations will work well here, but that is a question of mathematics, not MATLAB.

[Ankita kumari]

Thank you very much sir for replying to my question. I have just started using matlab and was given the task to plot the graph. I was facing problems so I put it here to get some solution. But apart from discouragement I haven't got anything. My question still remains unsolved. So, if you could help me what is the way to get the integral then, it would be quite helpful. My question was not for infinite domain, it was from minus infinity to some constant t.

[Walter Roberson]

minus infinity to some constant t is an infinite distance, so you are working in the infinite domain.

[Ankita kumari]

So how can I integrate that if not by using trapz?

[John BG]

'infinity is a big place' .. !? how do you know, have you been there?

Let be a static electric charge that generates a field with amplitude that decreases 1/R .. 1/R^2

the field is null at Infinity

Depending on the value of the charge the field may be null a couple feet away from the charge. 3 feet away and you have reached Infinity for that particular problem.

John

[e-mail]

[John D'Errico]

John - Infinity IS far away, if you are trying to use a tool like trapz. In fact, that makes the problem impossible to solve using trapz directly.

And I DID tell you how to solve the problem of an infinite integral. The use of a transformation is a classical solution.

Or, if you have an understanding of your problem, then you can truncate the problem.

Finally, you can use other tools, perhaps a Gaussian integration, chosen from a class appropriate for your specific problem. (There are lots of tricks one could try. Much depends on your mathematical abilities.)

Of course, all of these require some knowledge of both the specific problem, and some understanding of the mathematics. If you are trying to solve this type of problem, then it would seem one should understand the mathematics.

[Walter Roberson]

"Depending on the value of the charge the field may be null a couple feet away from the charge."

Only if you have shielding, or the initial charge is 0. Otherwise at any given distance you have reduced charge but not non-zero. Place two electrons at mutual rest a light year away from each other and they will affect each other.