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Topic: Calculus without calculus
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Subject:   Calculus without calculus
Author: LFS
Date: May 7 2011
No steps but at least answers in wolframalfa:
1. integral from 0 to infinity 2/(x+2)^3
2. area between 3-x^2 and -2x
3. integral x=-3 to x=3 of pi*(x^2-9)^2
(No keywords gave me the solid, I had to have the endpoints and integral formula
and know to NOT look at the graph.)

A little off topic
I really enjoyed this talk by conrad wolfram:
www.youtube.com/watch?v=60OVlfAUPJg

I want my (non-math) IT kids to do the cool things from calculus but without
having to know calculus. And in case you think this "doing without proving" is a
non-mathematical, please prove that the area of a circle is pi*r^2 without
calculus and yet we use this formula in 6th grade.

I use geogebra to calculate area under and between curves (using the command
Integral[]) and arc length (using command Length[]). This last is great fun for
e.g. the toboggan ride around the ellipse x^2/9+y^2/4=1 (I have them first check
if the Length[circle] gives them the circumference.) Of course we do all kinds
of extreme value problems, but the area and length problems are the most
interesting because you can "see" them, calculate other stuff like average
speed,...

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