Important: For each problem, you must show and fully justify each step of your solution and clearly indicate your answer. Your answers must be exact, fully simplified and reduced. If you happen to use a test for convergence or divergence in any problem, you must

1) clearly state the name of the test you are using and what the test says;

2) verify that the conditions of the test are met - be sure to show all of your work for this;

3) and clearly state the conclusion of the test for your problem.

When sketching graphs, be sure to fully explain how you obtained your graph including all algebraic steps. Also, be sure to label the exact coordinates (in t or in x and y as appropriate) of several points in your graph as well as including the direction of your graph if appropriate.

Question 3:

A: Use an appropriate trigonometric substitution to evaluate the integral x³ ( x² 4) dx for x > 2. Be sure to show and fully explain all of the steps of your integration.

B: How does your calculation in part A change if we instead consider values of x < 2?