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 See
odd & even functions
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.
Mentally Compute an Integral by Thinking "Hump"
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).
work & answers
instructions on integration with respect to x
© 2003, 2007, 2009 ,8/2019, 4/2020, 11/2022, 4/2023, A. Azzolino