Question

Problem 1

f(x) = ex * cos(x)

Evaluate the integral of f(x) from x = - Π / 2 to x = + Π / 2 using:

1. Trapezoidal Rule where Δx = Π / 6

2. Simpson's 1/3 Rule where n = 4

3. Simpson's 3/8 Rule

4. Draw a scatter plot of f(x) in Excel over the desired range (use sufficient data points to accurately depict the function)

5a. What is the true solution? (evaluate the integral)

5b. Find E_T and ε_T for each method in parts 1 through 3.

Problem 2

1. Use numerical integration to solve 5.17 in the textbook. Use Simpson's 1/3 Rule broken up into two segments to ensure all data is used.

2. Draw a scatter plot of the data from 5.17.

*Be sure to title each graph and include axis labels (with units if appropriate).

Answer 1