Consider the integral: ∫ π 0 (8 +4cos(x))dx. Perform all the following calculations by hand, showing all steps.
a) Solve the given equation analytically. (Round the final answer to four decimal places.)
b) Solve the given equation using a single application of the trapezoidal rule and determine the true percent relative error based on the analytical solution found in (a). (Round the solution of the equation to five decimal places and percent relative error to two decimal places.)
c) Solve the given equation using the composite trapezoidal rule with n = 2 and 4. Also, determine the true percent relative error based on the analytical solution. (Round the solutions of the equation to four decimal places and percent relative errors to two decimal places.)
d) Solve the given equation using the single application of Simpson’s 1/3 rule and determine the true percent relative error based on the analytical solution. (Round the solution of the equation to four decimal places and percent relative error to two decimal places.)
e) Solve the given equation using the composite Simpson’s 1/3 rule with n = 4 and determine the true percent relative error based on the analytical solution. (Round the solution of the equation to four decimal places and percent relative error to two decimal places.)
