Numerical Methods

Simpson's 1/3 rule is exact for polynomials up to degree 3. $\int_0^2 x^3 dx = [x^4/4]_0^2 = 16/4 = 4$. Using formula: $\frac{1}{3}[0 + 4(1) + 8] = \frac{12}{3} = 4$.