Greetings to all, could you help me with this integral please
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Greetings dear friends, I am trying to graph this integral so that I can obtain a graph x =f(t)
Thank you!
댓글 수: 4
John D'Errico
2022년 2월 17일
편집: John D'Errico
2022년 2월 17일
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?
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Torsten
2022년 2월 17일
편집: Torsten
2022년 2월 17일
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.
댓글 수: 4
David Goodmanson
2022년 2월 17일
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.
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