Chapter 4.3, Problem 26ES

To determine

To derive: The Simpson’s rule with error by using ${\displaystyle \underset{x_0}{\overset{x_1}{\int }}f\left(x\right)}dx=a_{0}f\left(x_0\right)+a_{1}f\left(x_1\right)+a_{2}f\left(x_2\right)+k{f}^4\left(\xi \right)$ and find the constants $a_0,a_1,a_2\text{ and }k$.