Chapter 21, Problem 3P

Evaluate the following integral:

${\displaystyle {\int }_{-2}^4\left(1-x-4x^3+2x^5\right)dx}$

(a) Analytically;

(b) Single application of the trapezoidal rule;

(c) Composite trapezoidal rule, with $n=2$ and 4;

(d) Simple application of Simpson's 1/3 rule;

(e) Simpson's 3/8 rule; and

(f) Boole's rule.

For each of the numerical estimates (b) through (f) determine the percent relative error based on (a).