Definite integral with complex number
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I need to solve an integral of the function f=(wn.*t).*exp(1i.*2.*pi.*t) where wn=1 and have complex numbers, it is a definite integral of 0 to 0.3 and I have to obtain a numeric answer. I tried to do with the comands int and integral but doesn`t help me because this comands uses symbolics variables and I need numeric answers, and I tried to obtain the sum under the wave but I couldn`t solve it. Can someone help me?
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Star Strider
am 18 Jan. 2017
Use the vpa function:
syms wn t
wn = sym(1);
f = (wn.*t).*exp(1i.*2.*pi.*t);
f_int = int(f, t, 0, 0.3)
f_int_num = vpa(f_int)
f_int =
- 1/(4*pi^2) - (((pi*3i)/5 - 1)*(1/4 + (2^(1/2)*(5^(1/2) + 5)^(1/2)*1i)/4 - 5^(1/2)/4))/(4*pi^2)
f_int_num =
0.012251815898938149373515863015179 + 0.038845017631697804582142824751429i
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Star Strider
am 18 Jan. 2017
To define ‘wn(t)’ as uniformly equal to 1 definitely changes the result:
syms wn t u_lim wn(t)
wn(t) = sym(1);
f = wn*exp(1i*2.*pi*t);
upper_limit = vpasolve(abs(int(f, t, 0, u_lim)) == 0.3, u_lim)
abs_upper_limit = abs(upper_limit)
upper_limit =
61.162453359143770665259861917249 - 0.1257699093208763500021861131513i
abs_upper_limit =
61.162582670939654308556507428042
Is the rest correct? Are you solving for the upper limit of integration that will make the integral equal to 0.3? If so, this works.
David Goodmanson
am 18 Jan. 2017
Bearbeitet: David Goodmanson
am 18 Jan. 2017
Hello Diana, symbolic variables are a great thing, but if you are looking for a numerical result and are happy with 15 or so sigfigs, it isn't like they have to be invoked. You can just do
ff = @(t,wn) (wn.*t).*exp(1i.*2.*pi.*t) % or you could define this in an mfile
integral(@(t) ff(t,1),0,.3) % pass in wn =1
format long
ans = 0.012251815898938 + 0.038845017631698i
Now that symbolic variables are much better integrated into Matlab, sometimes I wonder if they are getting overused.
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