Chapter 13.8, Problem 8E

(a)

To determine

To calculate: The approximate value of integral ${\displaystyle {\int }_0^1{x}^3}dx$ for $n=4$ by Trapezoidal Rule.

(b)

To determine

To calculate: The approximate value of integral ${\displaystyle {\int }_0^1{x}^3}dx$ for $n=4$ by Simpson Rule.

(c)

To determine

To calculate: The exact value of ${\displaystyle {\int }_0^1{x}^3}dx$ by integration.

(d)

To determine

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