Chapter 21, Problem 8P

Integrate the following function both analytically and numerically. For the numerical evaluations use

(a) Single application of the trapezoidal rule;

(b) Simpson's 1/3 rule;

(c) Simpson's 3/8 rule;

(d) Multiple application of Simpson's rules, with n = 5;

(e) Boole's rule;

(f) The midpoint method;

(g) The 3-segment–2-point open integration formula; and

(h) The 4-segment–3-point open integration formula.

${\displaystyle {\int }_0^3\left(5+3\cos x\right)dx}$

Compute percent relative errors for the numerical results.