% Matlab script int_script_template
% Integrates y = x.*2
% Steve Martel
% Date 8_26_04

% Set the increment dx
dx = 1;
%dx = 0.1;
%dx = 0.01;
% Set the domain of x (let x range from 0 to 10)
x = 0:dx:10;
% Determine how many values of x there are
n = length(x);
% Break the set of x-values into two sets,
% one that has all values but the last,
% the other that has all values but the first
x_beg = x(1:n-1);
x_end = x(2:n;
% Find the x-midpoints 
x_mid = (x_beg + x_end)/2;
% Calculate y at the values of x and x_mid
y = x.^2;
y_mid = x_mid.^2;
y_beg = x_beg.^2;
% Open up a figure window called "figure 1"
figure(1)
clf
% Plot the curve y = x.^2 on figure 1
plot(x,y)
hold on
stairs(x,y)
% Sum up the area of the rectangles to get the cummulative area
area_mid = cumsum(y_mid.*dx));
area_beg = cumsum(y_beg.*dx);
% Open up a figure window called "figure 2"
figure(2)
clf
% Plot the area under the curve y = x.^2 on figure 2
plot(x_mid,area_mid)
hold on
plot(x,(1./3)*x.^3,'r')