Asked by Pilar Jiménez
on 17 Jan 2017

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?

Answer by Star Strider
on 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

Pilar Jiménez
on 18 Jan 2017

Star Strider
on 18 Jan 2017

My pleasure.

Please let me know.

Star Strider
on 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.

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Answer by David Goodmanson
on 18 Jan 2017

Edited by David Goodmanson
on 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.

David Goodmanson
on 18 Jan 2017

Pilar Jiménez
on 18 Jan 2017

Yes, I will share with him to check it. Thanks for you support.

Pilar Jiménez
on 18 Jan 2017

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