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nvals
[10 30 50 100 1000]; % make array of possible n values:
=
j
= 1:length(nvals) %iterate over n values
n = nvals(j);
xvals = linspace(1,4, n+1); % returns an array of the interval 1 to 4
%divided into n+1 interval, i.e. our endpoints
for
4] so for left endpoints we want to
% xvals looks like [1 1.333
% toss the last point, right endpoints we want to toss the first
% in MATLAB, this is:
...
xvals_right = xvals(Z:end); % chops off first element
xvals_left = xvals(1:end-1); % chops off last element
deltax
f
=
(4-1)/n; % compute width of each rectangle
@(x) log(x); % define our function f using MATLAB syntax
=
f_right = f(xvals_right); % compute our right endpoint rectangle heights
f_left = f(xvals_left); % same for left
% notice we can put an array into a function, one of MATLAB’s strenghts
Rn
Ln
=
=
deltax*sum(f_right) % Rn = sum deltax
deltax*sum(f_left) % same for Ln
*
f(xj)
end
>>
riemann
n=
10
Rn=
2.7475
Ln=
2.3316
30
100
Rn=
2.5659
Ln=
2.5243
n=
1000
=2.5473
:n=
2.6139
n
\j’c,ILJ€
50
2. 5865
Ln
=
2.5034
n=
2.5431
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