function area = int_function_template(x_low,x_high,dx)
% function area = int_function_template(x,dx)
% Numerical integration of the function y = x.*2
% Input parameters
% x_low = lower limit of the domain of x
% x_high = upper limit of the domain of x
% dx = spacing of x-values
% Example
% x_low = 0;
% x_high = 10;
% dx = 0.1;
% area = int_function_template(x_low,x_high,dx);
% Steve Martel
% Date 8_26_04

% Create an array of x-vales from x_low to x_high
x = ;
% Determine how many values of x there are
n = ;
% 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_end = ;
% Calculate y at the values of x, x_beg, and x_end
y = ;
y_beg = ;
y_end = ;       % We don't use these values here
% Sum up the area of the rectangles to get the cummulative area
area = ;

% Plot figures

% Open up a figure window called "figure 1"
figure(1)
% Clear the figure
clf
% Plot the curve y = x.^2 on figure 1
plot(x,y)
% Keep the figure window to plot another curve
hold on
% Plot a red stairstep approximation of the curve
stairs(x,y,'r')
% Add title and labels to axes
title('y=x^2')
xlabel('x')
ylabel('y')

% Open up a figure window called "figure 2"
figure(2)
% Clear the figure
clf
% Plot the analytical solution for the area
plot(x,(1/3)*x.^3)
% Keep the figure window to plot another curve
hold on
% Plot the area under the curve y = x.^2 on figure 2
plot(x_end,area,'r')
% Add title and labels to axes
title('Area under y=x^2 and numerical approximation (red)')
xlabel('x')
ylabel('y')