# Integrate inside ode45, every value of a a vector

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Ilias Minas on 1 Mar 2020
Commented: darova on 1 Mar 2020
Hi everyone,
I have the following part inside a script
if t<=1.5
x=(0:2.51326406981556e-05:2*pi)'; %limits for integration
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for i=1:1:250001
Y=(((r.*cos(x)-y(5))-r.*cos(x)+y(6))./((((((r.*cos(x)-y(5))-r.*cos(x)+y(6))).^2+((r.*sin(x)-y(5))+r.*sin(x)).^2).^0.5))); % r is difined in the beginning of the script
Integral(i)=trapz(x,Y);
end
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y(5)=y(6);
I want after every time step, which is 1e-5, to use the values of y(5) and y(6) in order to calculate the Integral(i) and use this value for the next calculation of y(5) and y(6).
Practically, i want to integrate every value of Y, which is a function of y(5), y(6), inside [0,2pi], and y(5) and y(6) to be calculated based on this integral.
Is this the correct way for doing this?
Thank you very much.

darova on 1 Mar 2020
no need of for loop
if t<=1.5
x=(0:2.51326406981556e-05:2*pi)'; %limits for integration
Y=(((r.*cos(x)-y(5))-r.*cos(x)+y(6))./((((((r.*cos(x)-y(5))-r.*cos(x)+y(6))).^2+((r.*sin(x)-y(5))+r.*sin(x)).^2).^0.5))); % r is difined in the beginning of the script
% C1 = r*cos(x) - y(5) + y(6) - r*cos(x);
% C2 = 2*r.*sin(x)-y(5);
% Y=C1./sqrt(C1.^2+C2.^2); % r is difined in the beginning of the script
IntegralY=trapz(x,Y);
end
Show the equations you use
darova on 1 Mar 2020
Here is what i have for tend=1.5e-02
dashed line: using trapz
solid line: integral=1    