Answer the following questions:

1) Integrate the function f(x) = 5 + cos(x) on the interval [0,4] analytically.

2) Estimate, numerically, the integration of f(x) = 5 + cos(x) using the following methods on the interval [0, 4]:

(a) single application of the trapezoidal rule;

(b) multiple application of trapezoidal rule with n=4;

(c) Simpsons 1/3 rule;

(d) Simpsons 3/8 rule;

(e) multiple application of Simpsons 1/3 rule with n =4; and

(f) Booles rule

3) compute the true relative percentage error in 2.(b) based on the true value computed in 1).