Editing Simpson's rule (section)

==== Undetermined coefficients ====
The third derivation starts from the ''[[ansatz]]''
<math display="block">\frac{1}{b - a} \int_a^b f(x)\, dx \approx \alpha f(a) + \beta f\left(\frac{a + b}{2}\right) + \gamma f(b).</math>

The coefficients {{math|α}}, {{math|β}} and {{math|γ}} can be fixed by requiring that this approximation be exact for all quadratic polynomials. This yields Simpson's rule. (This derivation is essentially a less rigorous version of the quadratic interpolation derivation, where one saves significant calculation effort by guessing the correct functional form.)