# How to take an integral symbolically and then convert it to type double?

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L'O.G. on 16 May 2023
Commented: Walter Roberson on 16 May 2023
How do I take the following integral symbolically? And convert it to double? I have a 1000 x 1 numeric vector of type double for A(t).
The following takes a minute or two to run and I'm not sure how to plot it to check.
syms t omega real
int(A*sin(omega*t),0,2*pi/omega)
L'O.G. on 16 May 2023
Thank you. I think the symbolic aspect is confusing me, so I am trying to do it in a more straightforward numerical approach.
Walter Roberson on 16 May 2023
format long g
syms t omega real
A = rand(5,1)
A = 5×1
0.988717788679954 0.961075790428598 0.548371988302065 0.728110260321502 0.293761135174945
Asym = sym(A);
symbolic_result = int(Asym*sin(omega*t),0,2*pi/omega)
symbolic_result =
omega = abs(randn())
omega =
1.29628039951883
numeric_result = integral(@(t) A .* sin(omega.*t), 0, 2*pi./omega, 'Arrayvalued', true)
numeric_result = 5×1
1.0e+00 * -2.20309881449055e-16 4.33680868994202e-17 -5.55111512312578e-17 -2.91433543964104e-16 -6.11490025281825e-17
Zero to within round-off error.

VBBV on 16 May 2023
Edited: VBBV on 16 May 2023
syms t omega real
A = rand(1000,1);
% specify the integration variable t as the argument
I = double(vpa(int(A.*sin(omega*t),t,0,2*pi/omega),2))
I = 1000×1
0 0 0 0 0 0 0 0 0 0
VBBV on 16 May 2023
Assuming some random data, you can specify the integration variable t as the argument and do symbolic integration

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