Write a function using lgwt() to calculate composite Gausian quadrature using the call I = compositeGauss_integrate(Fun,a,b,n,N) where, - Fun is the name for the function to be integrated, - a is the lower limit of integration, b is the upper limit of integration, - n is the number of points used in each Gaussian quadrature subintervals - N is the number of subintervals
Write a function using lgwt() to calculate composite Gausian quadrature using the call I = compositeGauss_integrate(Fun,a,b,n,N) where,
- Fun is the name for the function to be integrated,
- a is the lower limit of integration, b is the upper limit of integration,
- n is the number of points used in each Gaussian quadrature subintervals
- N is the number of subintervals.
Code:
function[I]=compositeGauss_integrate(Fun,a,b,n,N)
% Inputs:
% Fun - the function being integrated
% a - the lower limit of the integration
% b - the upper limit of the integration
% n - the number of points used in each Gaussian quadrature subintervals
% N - the number of subintervals
% Outputs:
% I - value of integral
% calculate the width of each subinterval
h=(b-a)/N;
% calculate the endpoints of the N subintervals
xs= ;
% initialize the integral value
I=0;
% for each subinterval, calculate the Gaussian point locations and the weights,
% then calculate the weighted sum of the evaluated function at the
% Gauss points and add it to the accumulated integral value
loop from the start of the first subinterval to the start of the last subinterval
x1= ; %start of subinterval
x2= ; %end of subinterval
% calculate Gauss points and weights in subinterval k
[x,w]=lgwt(n,x1,x2);
% add weighted sum of evaluated function to accumulated integral
I=I+sum(Fun(x).*w);
end
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