Chapter 8.6, Problem 44E

(a)

To determine

To calculate: The integral ${\displaystyle {\int }_0^{2}f\left(x\right)dx}$ using the Trapezoidal rule and Simpson’s rule.

(b)

To determine

To calculate: The model of the form $y=a{x}^3+b{x}^2+cx+d$ and also integrating the resulting polynomial over $\left[0,2\right]$ interval also compare the integral result with part (a).