integrate_e^(2x)

function [ trap, simp ] = integrate_e(N)

    a= -1;
    b= 5;
    x= a:((b-a)/N):b;
    f= exp(2 * x);

    Iexact = 11013.16522976174;
    trap = 0;
    simp = 0;

    for k=1:N  %Note that the vector f has (N+1) elements
        trap = trap+((b-a)/N)*(f(k)+f(k+1))/2;
    end

    for k=1:(N/2)
        simp = simp + ((b-a)/N)/3*(f(2*k-1)+4*f(2*k)+ f(2*k+1));
    end

    fprintf('            Exact integral = %f.\n', Iexact)
    fprintf(' Trapezoidal approximation = %f.\n', trap);
    fprintf('     Simpson approximation = %f.\n', simp);fprintf('\n')

    trap_error = abs(trap-Iexact);
    simp_error = abs(simp-Iexact);

    fprintf(' Trapezoidal error = %f.\n', trap_error);
    fprintf('     Simpson error = %f.\n', simp_error);

end