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

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Lewis HC
Lewis HC 2022-2-17
评论： Lewis HC 2022-2-18
Greetings dear friends, I am trying to graph this integral so that I can obtain a graph x =f(t)
Thank you!
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John D'Errico
John D'Errico 2022-2-17
编辑：John D'Errico 2022-2-17
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
Lewis HC 2022-2-17
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

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Torsten
Torsten 2022-2-17
编辑：Torsten 2022-2-17
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.
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David Goodmanson
David Goodmanson 2022-2-17
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
Lewis HC 2022-2-18
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!

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