Write a MATLAB program to perform the integration of a quarter circle.

Write a MATLAB program to perform the integration of this quarter circle (radius = 4 units) using the trapezoid method. Since the equation of a circle is x^2+y^2=r^2 , the equation of the quarter-circle as shown is y= sqrt(r^2-x^2) . Calculate the value of pi by dividing the area of the circle (the integral times four) by the radius squared ( ). Your MATLAB program should prompt the user for the number of increments to be used in the integration and should print out the value of pi to five decimal places.

[Walter Roberson]

What is your question?

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Meredith Umphlett]

I need help on making a MATLAB progam to find the area of a quarter circle... this is what I have so far.

ni = input('Enter number of intervals');

lowlim = 0;
uplim = 4;

inc = input('Enter the number of increments');

A = 0;

for k = 1:(ni+1)
    x(k) = lowlim + (k-1)*inc;
    y(k) = sqrt(16-x(k));
    
    if k > 1
        A = A + .5*(y(k) + y(k-1))*inc;
    end
end
% Print the area to the screen
fprintf('\nThe area is %.5f\n\n',A)

[Walter Roberson]

Are you using the trapezoid rule? If you are then I do not see your contributions for the first and last point.

[Meredith Umphlett]

Yes I am. These are my modifications.

lowlim = 0;
uplim = 4;
r =4;


ni = input('Enter the number of increments');

inc = (uplim-lowlim)/ni;

A = 0;

for k = 1:(ni+1)
    x(k) = lowlim + (k-1)*inc;
    y(k) = sqrt(16-(x(k)^2));
     
    
    if k > 1
        A = A + .5*(y(k) + y(k-1))*inc;
    end
end
% Print the area to the screen
Area = A*4
fprintf('\nThe area is %.5f\n\n',Area)

pie = (Area)/(r^2);
fprintf('\nPie is equal to %.5f\n\n',pie)

[Walter Roberson]

Is there a reason you are not using trapz() or cumtrapz() ?

x = linspace(lowlim, uplim, ni);
y = sqrt(16-(x.^2));

now caculate the area in vectorized ways