helleman

fprintf('Question #3:\n');
t = [1 2 3.25 4.5 6 7 8 8.5 9.3 10]; %time (s)
v = [5 6 6.6 7 8.5 8 6 7 7 5]; %speed (m/s)
d = trapz(t,v); %distance traveled from t = 1 to t = 10
fprintf('Using the trapezoidal rule:\n\t%2.4f m are covered from t = 1s to t = 10s\n',d);
pC = polyfit(t,v,3); %coefficients of cubic fit for v vs t
fC = @(x) polyval(pC,x);
tC = [1 5.5 10];
vC = polyval(pC,tC);
ISimpson = (4.5/3)*(vC(1)+4*vC(2)+vC(3));
fprintf('Using Simpson''s 1/3 rule:\n\t%2.4f m are covered from t = 1s to t = 10s\n',ISimpson);
IClassic = integral(fC,1,10);
fprintf('Using classical integration techniques:\n\t%2.4f m are covered from t = 1s to t = 10s\n',IClassic);
fprintf('Simpson''S 1/3 rule and classical integration techniques produce identical results\n');