Consider $f(x) = \cos(x)$ and the points $x_0 = \pi/2$, $x_1 = \pi/4$ and $x_2=3\pi/4$. Consider $f(x_i)$ with 5 decimal places. Find an estimate for the error of integration when you use Simpson's rule to calculate the integral of f between $x_1$ and $x_2$.
I did
$$E(f) < |\frac{b-a}{180}||\frac{b-a}{N}|\max_{[x_1,x_2]} |f^{(4)}| = 0.0023479$$
Is this correct?
Is the reason I am given 3 points that I need an even number of intervals to use Simpsons rule and is that why I set N = 2 and not 1?