Trapezoidal Rule

Find the integration $\int_a^b f(x) dx$, using trapezoidal rule.

f = @(x) x.^2;
a = 0; b = 1; n = 100;
h = (b-a)/n;
x = a:h:b;
fx = f(x);
trap = (2*sum(fx(2:n))+fx(1)+fx(n+1))*h/2

trap =  0.33335

%plot gnuplot
plot(x,fx)

Try yourself

Find the integration $\int_a^b f(x) dx$, using simpson's rule.