Can you solve these puzzles and problems from the Australian Mathematical Gazette?

Professor Higgins is now a regular feature writer in the AMG; click the links to the problems and see if you can solve them yourself.

This material appears courtesy of the Australian Mathematical Gazette Puzzle Corner.

Derivative vs Integral - the final slapdown...

It's a haunting, age-old debate...which is better? The Derivative or the Integral? 

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© 2014 by Professor Peter Higgins.