Calculate right-hand Riemann sum in https://math.stackexchange.com/q/2618369/290189 graph: https://i.stack.imgur.com/5TSH5.png

rrsum.m

Nvec = 10000:10000:1000000;  % no of intervals
rrsumvec = zeros(size(Nvec));
for ind = 1:length(Nvec)
    N = Nvec(ind);
    dx = 5 / N;
    x = (1:N) * dx;
    fx = sqrt(25 - x.^2);
    rrsum(ind) = sum(fx * dx);
end
 
% plot the graph
figure
hold on
title("Numerical riemann sum vs theoretical value")
plot(Nvec,25*pi/4*ones(size(Nvec)),"-r");
plot(Nvec,rrsum,"-b");
legend("Theoretical","Numerical")
legend("location", "southeast")
hold off