Quick questions on Simpson's rule for numerical integration in QCE Specialist Mathematics Unit 4

The pattern of coefficients is $1, 4, 2, 4, 2, \dots, 4, 1$. The first and last are $1$, every odd-position interior value is $4$, every even-position interior value is $2$, and the values at odd positions always outnumber those at even positions. This pattern is why $n$ must be even: the points group into pairs of strips, each capped by a parabola.

$h = \dfrac{1 - 0}{4} = 0.25$, so $x_0 = 0$, $x_1 = 0.25$, $x_2 = 0.5$, $x_3 = 0.75$, $x_4 = 1$.

$4(0.939413) = 3.757652$; $\;2(0.778801) = 1.557602$; $\;4(0.569783) = 2.279132$. Sum: $1 + 3.757652 + 1.557602 + 2.279132 + 0.367879 = 8.962265$.

The accepted value is about $0.74682$, so the estimate is accurate to four decimal places with only four strips, as expected of Simpson's rule.