how to convert vectore to function before integral

im working on a project and the whole time i worked with vectors that shows the numbers of function, but now i want to integral the function, and i cant integral the vector, i cant use trapez, it give whrong unswear too.

%% Q1part1
T0=20;
T1=5;
w0=(2*pi)/T0;
x= exp(-1*abs(t));
for n=1:601
    if n>100
        x(n)=0;
    end
end
for n=1:601
    if n>200
        x(n)=x(n-200);
    end
end
figure(1)
plot(t,x)
xlim([-5 55])
%% Q1part3
fun = @(x,n) exp(-abs(x)-1i*x.*n.*w0);
c=[1:1:81];
t=[-40:1:40];
helper=[1:1:81];
for n=1:81
   c(n) = 0;
    helper(n) = 0;
helper(n) = integral(@(x) fun(x,n-41),-5,5);
helper(n)=helper(n)./20;
if abs(imag(helper(n)))<0.01
    c(n)= real(helper(n));
end
end
figure(2)
plot(t,c)
%% Q1part6
figure(345345)
plot(t,x)
function [EN] = integralfor6(n,x,c)
t=linspace(-5,55,601);
x_n=0; 
T0=20;
w0=(2*pi)/T0;
% X=@(t) exp(-2*abs(t))
x=x.*x
figure(8888)
plot(t,x)
for i=-n:n
    x_n = x_n+(c(i+40)*(cos(i*w0*t)));
end
end

[darova]

I don't see any trapz funciton. Can you show it?

[Jonathan Jubran]

im not allowed to use it

Answer 1

[Sulaymon Eshkabilov]

Your code contains a few potential errs that have been corrected.

%% Q1part1
T0=20;
T1=5;
t=linspace(-5, 55, 601);
w0=(2*pi)/T0;
x= exp(-1*abs(t));
for n=1:601
    if n>100
        x(n)=0;
    end
end
for n=1:601
    if n>200
        x(n)=x(n-200);
    end
end
figure(1)
plot(t,x)
xlim([-5 55])
%% Q1part3
fun = @(x,n) exp(-abs(x)-1i*x.*n.*w0);
c=1:81;
t=-40:40;
helper=1:81;
for n=1:81
   c(n) = 0;
   h(n) = 0;
%    helper(n) = 0;
helper(n) = integral(@(x) fun(x,n-41),-5,5);
helper(n)=helper(n)./20;
H(n) = quad(@(x) fun(x,n-41),-5,5);  % Quad is also tested
if abs(imag(helper(n)))<0.01
    c(n)= real(helper(n));
end
if abs(imag(H(n)))<0.01
    h(n)= real(H(n));
end
end
figure(2)
plot(t,c, 'r'), title('Integral @')
figure(3)
plot(t, h, 'b'), title('Quad @')
%% Q1part6
[X,t] = integralfor6(n,x,c);
figure(4)
plot(t,X)
function [x_n,t] = integralfor6(n,x,c)
t=linspace(-5,55,601);
x_n=0; 
T0=20;
w0=(2*pi)/T0;
% X=@(t) exp(-2*abs(t))
x=x.*x;
figure(5)
plot(t,x)
for i=1:n-40
    x_n = x_n+(c(i)*(cos(i*w0*t)));
end
end

Note that quad() is also tested.

Good luck.