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.

work & answers instructions on integration with respect to x

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