In our first class we were introduced to Scientific Notebook. Please complete the following assignment using this program. All of your work should be typeset. Be sure to include your name, date, and a heading.
Integration by parts is a very powerful method to obtain formulas for integrals.
A special application of this method is the derivation of recursive formulas.
Consider the following integral.
where
is a positive integer
The goal is to use integration by parts to find an expresion for I(n) in terms of I(n-1)
(ie. a recursive formula).
1. Compute I(0), I(1), and I(2).
2a. How does I(1) depend on I(0)?
2b. How does I(2) depend on I(1)?.
3. Can you see a pattern emerging?
Write
) in
terms of
Extra Credit: use induction to prove your formula!
This document created by Scientific Notebook 4.0.