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

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sirihaas gaddipati
sirihaas gaddipati 2020-3-12
编辑： sirihaas gaddipati 2020-3-22
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);

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回答（1 个）

Raynier Suresh
Raynier Suresh 2020-3-18
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

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