riemann sum for area of circle with range x and equation of the circle

r=10;

ezplot(@(x,y) (x).^2 +(y).^2 -r^2, [-10,10]);

axis equal

%title "circle centered at (0,0) with radius of 10"

dx=4;

x=-10:dx:10;

y=(100-(x).^2).^(1/2);

sum=sum(2*y*dx);

[darova]

How does it work? What about trapz?

Answer 1

[Raynier Suresh]

To find area using riemann sum you could use the following code,

r = 10; % Radius 
x = -r:0.01:r; % Range of x 
y = sqrt(r*r - x.*x); % y = f(x) 
Area = 2*sum(y) % sum(y) will give the area of semi circle 
plot(x,y);hold on;plot(x,-1*y);

To solve using integration directly,

r = 10; % radius 
y = @(x)sqrt(r.*r - x.*x); % y = f(x) as function handle 
Xmin = 0; 
Xmax = r; 
area = 4*integral(y,Xmin,Xmax) % Xmin and Xmax correspond to the first quarter of circle