Question

please use matlab/get someone with a matlab license

Problem 3: Find the value of the integral 0 using the rectangle rule with spacing Δ:: 0.01. Use the code for the rectangle quadrature rule developed in the class

Answer 1

dx =0.01;%spacing
x=0:dx:10;%x grid
fx=@(x)cos(x)+x.^2.*exp(-x.^2);
N=(10-0)/dx;
Fx=0;%variable to store integral
for i=1:N
Fx = Fx + dx*fx((x(i)+x(i+1))/2);
end
Fxinteg=integral(fx,0,10);% computed using inbuild matlab
%integral function to check accuracy of computed integral
disp('integral computed using rectangle quadrature is');
disp(Fx);
disp('integral computed using in-built function is');
disp(Fxinteg);

MATLAB output

integral computed using rectangle quadrature is
-0.100909914924232

integral computed using in-built function is
-0.100907648162991