## Exercises

1. Use integration by parts to perform the following integrations. Make your choices for u and dv clear. Your answers should not contain any integrals, so you will have to use the intparts command repeatedly.

2. Suppose m and n are positive integers. Can you conjecture general formulas for the following integrals? Actually proving your conjectures would require the use of mathematical induction, and I'm not asking you to go that far.
3. Find an integral of simple form that Maple can't do. It shouldn't be hard, since most integrals can't be done analytically. (If Maple can't do an integral analytically, then it just returns the integral unevaluated.)

A definite integral can be evaluated numerically, by using the evalf command outside the int command. Try this with your integral. For your report, come up with at least two reasons why an analytical answer is better than a numerical one, if you can get it.

4. In differential equations, one often has to solve for what is called the particular solution. For example a particular solution of the differential equation

is . What we mean by solution is that the differential equation is satisfied if you substitute into it. Find a particular solution of the differential equation

Hint - try , where A and B are constants. Can you choose values of A and B so that satisfies the differential equation?

William W. Farr
Fri Aug 25 18:22:38 EDT 1995