Formatting an input set of Values

In my Gauss Quadrature code, it requests 4 values be entered as inputs. I know what 3 of the 4 inputs are, but the first input is the entire base function. I am having two issues:

The first issue is I am struggling to properly format my input function so that it uses the correct equation

The second issue is if the code doesn't result in an error regarding the function, it comes up with an error saying I need to define my x and y values. Does anyone have a solution?

The function in question is:

sqrt(x'(t)^2 + y'(t)^2) integrated from a to b where a = 0 and b = 5

Posted below is my code:

%Integration using Gauss-Legendre quad

%Similar to 'integral' in MATLAB

function y=GLGD_int(fun,xmin,xmax,n)

%fun: the integrand as a function handle

%xmin: lower bound of integration

%xmax: upper bound for integration

%n: order of polynomials used

[x_IP,weight]=GLGD_para(n);

%assign global coordinates to the integration points

x_eval=x_IP*(xmax-xmin)/2+(xmax+xmin)/2;

y=0;

for aa=1:n

y=y+feval(fun,x_eval(aa))*weight(aa)*(xmax-xmin)/2;

end

end

function [x_IP,weight]=GLGD_para(n)

%n: order of the polynomial

x_IP=legendreRoot(n,10^(-16));

weight=2./(1-x_IP^2)./diff_legendrePoly(x_IP,n).^2

end

%roots of the Legendre Polynomial using Newton-Raphson

function x_IP=legendreRoot(n,tol)

%n: order of the polynomial

%tol: tolerance of the error

if n<2

disp('No root was found');

else

root=zeros(1,floor(n/2));

for aa=1:floor(n/2) %iterate to find half of the roots

x=cos(pi*(aa-0.25)/(n+0.5));

err=10*tol;

iter=0;

while (err>tol)&&(iter<1000)

dx=-legendrePoly(x,n)/diff_legendrePoly(x,n);

x=x+dx;

iter=iter+1;

err=abs(legendrePoly(x,n));

end

root(aa)=x;

end

if mod(n,2)==0

x_IP=[-1*root,root];

else

x_IP=[-1*root,0,root];

end

x_IP=sort(x_IP);

end

end

%derivative of the Legendre Polynomial

function y=diff_legendrePoly(x_IP,n)

%x_IP: coordinates of integration points

if n==0

y=0;

else

y=n./(x_IP.^2-1).*(x_IP.*legendrePoly(x_IP,n)-legendrePoly(x_IP,n-1));

end

end

%Produces Legendre Polynomials

function y=legendrePoly(x,n)

%x: input x

if n==0

y=1;

elseif n==1

y=x;

else

y=((2*n-1).*x.*legendrePoly(x,n-1)-(n-1)*legendrePoly(x,n-2))/n;

end

end

[Uday Pradhan]

The function in question is:

sqrt(x'(t)^2 + y'(t)^2) integrated from a to b where a = 0 and b = 5

So, x and y are functions of t, right? You need to define these to get rid of the errors.