Write a userdefined function called midpointMEm except repla

Write a user-defined function called \"midpointME.m\" (except replace ME with your initials) that evaluates the following integral within a specified tolerance, using the Rectangle/Midpoint Rule. The function takes two inputs: the maximum relative tolerance allowed in the approximation, and a vector of the limits of integration (i.e. [a, b]). The function produces one output: the approximate value of the integral. integral^b_a x e^-x^2/sin(x) dx

Solution

function value = midpointME( a , b , maxRelativeTolerance )
    %tolerance in terms of relative error
    N = 5;
    lastAnswer = 1000000;
    while 1
        h = (b - a)/N;
        answer = 0;
        xn = a;
        for i=0:N-1
            %find value for xn
            answer = answer + xn*exp( (-xn*xn)/sin(xn) );
            xn = xn + h;
        end
        answer = answer*h;

        relativeError = abs( lastAnswer - answer)/abs( lastAnswer );
        if relativeError < maxRelativeTolerance
            value = answer;
            break;
        end;
        lastAnswer= answer;
        N = N + 1;
    end
   %sample call : midpointME( 1, 2, 0.5 )