Greetings to all, could you help me with this integral please

Greetings dear friends, I am trying to graph this integral so that I can obtain a graph x =f(t)

Thank you!

[Torsten]

Not clear what you mean.

The integral will be a function of t and x: I = F(x,t).

Now what do you want to plot ?

[Lewis HC]

I need to plot that function, dear friend

[John D'Errico]

Plot as a function of WHAT? What will be plotted on each axis? Since you want to integrate over w, that still leaves TWO variables, x and t. And while you seem to think you can plot x on the x axis, and t on the y axis, that makes no sense, since you are asking to plot the INTEGRAL. x = f(t) makes no sense in this context, because there is no functional relationship there, not even an implicit one.

Worse, since there is a complex component in this, what will you plot assuming the result is complex? The real or the imaginary part? And how does the integral factor in?

[Lewis HC]

I want to do something similar to what you can see from minute 5 of this video:

https://www.youtube.com/watch?v=OGyMOmph8vw

Thank you dear John

Answer 1

[Torsten]

t = linspace(0.1,3,29);
x = linspace(-3,3,60);
[T,X] = meshgrid(t,x)
for i = 1:numel(x)
    for j = 1:numel(t)
        f = @(w) 1/pi*sin(w)./w.*exp(-T(i,j)*w.^2).*cos(w.*X(i,j));
        I = integral(f,-Inf,Inf);
        F(i,j) = I;
    end
end
surf(T,X,F)

You only need to consider the real part of the integrand since the imaginary part is an odd function of w, thus with integral = 0.

[Lewis HC]

Thank you very much dear friend, I am trying to enter the code but I get an error

[Torsten]

What's the error you get ?

[David Goodmanson]

Hi Luis,

or you could replace the for loops with

F = (1/2)*( erf((X+1)./(2*sqrt(T))) -erf((X-1)./(2*sqrt(T))) );

and get the same result.

[Lewis HC]

Greetings to all, thank you very much for the support provided dear friends, you helped me with my problem in the most precise way, you are the best, thank you!