Chapter 13.8, Problem 12E

(a)

To determine

To calculate: The approximate value of integral ${\displaystyle {\int }_0^2{x}^{3/2}}dx$ for $n=8$ by Trapezoidal Rule.

(b)

To determine

To calculate: The approximate value of integral ${\displaystyle {\int }_0^2{x}^{3/2}}dx$ for $n=8$ by Simpson Rule.

(c)

To determine

To calculate: The exact value of ${\displaystyle {\int }_0^2{x}^{3/2}}dx$ by integration.

(d)

To determine

The most accurate approximation rule among the Trapezoidal rule and Simpson Rule.