Chapter 5.2, Problem 4E

Apply the composite Simpson’s Rule with $m=1$, 2, and 4 panels to the integrals, and report the errors.

1. ${\displaystyle {\int }_0^{1}x{e}^{x}dx}$
2. ${\displaystyle {\int }_0^1\frac{dx}{1+x^2}dx}$
3. ${\displaystyle {\int }_0^{\pi }x\cos xdx}$