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I am trying to approximate the solution to:

$\int_{0}^{t} f(s) db(\omega,s) = f(s)b(\omega,s)|^{t}_{0} - \int_{0}^{t} f'(s) b(\omega,s) ds$

where $f(t) = sin(t)$ and $t \in [0,2\pi]$ for both sides of this equation.

My code for the left side is:

N = 2000;  Tend = 2*pi;  dt = Tend/N;  t = 0:dt:Tend;
f = sin(t)*sqrt(dt);
f = [0 ff(1:end-1)];
[fL,junk] = meshgrid(f,1);
dW = cumsum([0 randn(1,N)].*fL,2);

but I can't figure out the right side at all, which is much harder. Can anyone help?

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