integral2 failing to calculate area of a square inside a circle?

Hello all,

I am integrating the area contained within a square and a circle using integral2. I use a circle centered at (0,0) with radius 2.75 and two squares with edge 0.5 (blue on image) and 1 (red on the image), whose bottom left corner lies on (0.5, 0.5). As the circle is larger than the squares, I would expect the result of the integral to be the areas of each square, 0.25 for the blue and 1 for the red. However, the output for the red one is 0.75. Am I missinterpretating the result?

Thanks in advance!

The image:

The code:

Zfun1 = @(x,y) double((x.^2 + y.^2) <= 2.75); % Circle function
integral2(Zfun1,0.5,1.5,0.5,1.5,'Method','iterated',...
    'AbsTol',1e-5,'RelTol',1e-5)  % Red square

integral2(Zfun1,0.5,1,0.5,1,'Method','iterated',...
    'AbsTol',1e-5,'RelTol',1e-5) % Blue square

rectangle1 = [0.5 , 0.5;  % Coordinates red square (for plotting)
             0.5 , 1.5;
             1.5 , 1.5;
             1.5 , 0.5;
             0.5 , 0.5];
rectangle2 = [0.5 , 0.5;  % Coordinates blue square (for plotting)
             0.5 , 1;
             1 , 1;
             1 , 0.5;
             0.5 , 0.5];
figure
circle(0,0,2.75); % circle
hold on; grid on
plot(rectangle1(:,1),rectangle1(:,2),'-.r'); % red square
plot(rectangle2(:,1),rectangle2(:,2),'-.b'); % blue square
axis equal
xlim([-0.1 2.8])
ylim([-0.1 2.8])
function h = circle(x,y,r)
    hold on
    th = 0:pi/50:2*pi;
    xunit = r * cos(th) + x;
    yunit = r * sin(th) + y;
    h = plot(xunit, yunit);
    hold off
end

Answer 1

[Tarunbir Gambhir]

Please correct the equation of the circular region in function 'Zfun1'. It should be of the form, x^2+y^2<=r^2.

[Jesus Sanchez]

Yes, I see I had that mistake. Now everything is working as it should. Thank you!