# Definite integral with an exponential

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Pilar Jiménez on 18 Jan 2017
Commented: Star Strider on 23 Jan 2017
I need to integrate this function f=wn.*exp(1i.*2.*pi.*t) to get the numerical result, where the variable function is t, and wn=1. Evalue limits are 0 to 0.9. Can somebody help me?

#### 1 Comment

Star Strider on 18 Jan 2017
See Definite integral with complex number for the context here.

Star Strider on 18 Jan 2017
Your question seems to have changed. With respect to ‘wn(t)’ see my Comment in your original Question.
Try this:
syms wn t u_lim wn(t)
wn(t) = sym(1);
f = wn*exp(1i*2.*pi*t);
cplx_int = int(f, t, 0, 0.9)
cplx_int_n = vpa(cplx_int)
abs_cplx_int_n = abs(cplx_int_n)
cplx_int =
-(5^(1/2)*1i + (10 - 2*5^(1/2))^(1/2) - 3i)/(8*pi)
cplx_int_n =
- 0.093548928378863903321291906615298 + 0.03039588939177436951706748797891i
abs_cplx_int_n =
0.098363164308346596734748787414694

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Star Strider on 19 Jan 2017
My pleasure.
See if this does what you want:
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)) == 0.9, u_lim)
abs_upper_limit = abs(upper_limit)
upper_limit =
61.226816497040968522581307264603 - 0.27736049247340612832400314608506i
abs_upper_limit =
61.227444722159630445299229455761
This is my previous code with 0.9 replacing 0.3.
Pilar Jiménez on 23 Jan 2017
Good day, I want to apologize to you because it seems to have an incorrect data that made my integral did not show the expected result. The problem has already been solved, thank you very much for your help.
Star Strider on 23 Jan 2017
My pleasure.