function [area, error] = trapezoidIntegrate(dx)
xMin = 0; % minimum x value
xMax = pi/2; % maximum x value
x = xMin:dx:xMax; % all x values
%1) Compute a y vector to be the sine of each element of the x vector.
%2) Plot x versus y
%3) Compute the approximate area under the curve as the sum of the
% trapezoids bounded by each adjacent pair of points and the x axis.
% Essentially, you'll average the height (y) of the pair and multiply
% by the width between them. Finally, you'll sum these values.
% Hint: Perform all of these operations using vectors so that you can
% make use of Matlab's sum function.
exactArea = -cos(xMax) - -cos(xMin);
error = exactArea - area;
disp(sprintf('From %g to %g with step %g, the approximate area is %g.', xMin, xMax, dx, area))
disp(sprintf('The actual area is %g, so the error is %g\n', exactArea, error))
end