### Integration

 Arithmetic Tricks, Rules & Shortcuts In Words & Symbols

• Factor-Out A Constant

• Switch the Limits and Get the Opposite

• Use Integration to Compute the Area Bounded by the Curves

• Simplify Through Symmetry

• Rewrite Using Zero As A Limit, If Possible

• Rewrite as A Sum By Seperating Terms

• Rewrite as A Sum By Using More Limits of Integration

• Use Basic Geometry Rather Than Calc to Complete the Integration.
• Consider Using a Function in y rather than a Function in x.  1. Begin the transition of orientation from y = f(x) and y = g(x) to x = f(y) and x = g(y) by writing the integration using y-limits rather than x-limits.   2. Continue the transition of orientation by rewriting two equations. a. y = f(x) x = f(y) b. y = g(x) x = g(y)   3. Write the integral expression, usually "top" function (furthest from the axis), "bottom" function (closest to axis).   4. Integrate.

 © 2003, 2007, 2009 ,8/2019, 4/2020, A. Azzolino   www.mathnstuff.com/math/spoken/here/2class/420/anti.htm