DUE: Friday 2 November
Format Two to three typed pages. (Note: MS Word has an "Equation" editor for typing equations.) Certainly, formulas will be part of your report, but the formulas should be relevant to the descriptions in the text.
Problem: The web page allows you to use Mathematica(TM) to compute antiderivatives. For example, if you type
(Sin[x])^2 * (Cos[x])^3
In the box, the antiderivative,
Sin[x]/8 - (1/48)Sin[3x] -(1/80)Sin[5x]
appears. On the other hand, typing
(Sin[x])^n * (Cos[x])^m
gives a complicated answer involving the Hypergeometric function.
For this project, investigate the antiderivative of
(Sin[x])^n * (Cos[x])^m
for various combinations of n and m. For which combinations can you give a simple formula for the antiderivative? Can you spot any general patterns? Justify as many of your observations as possible.