Integration

• 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.

    answers       answers       answers

• Mentally Compute an Integral by Thinking "Hump"
  

  Swipe between stars for answers. * a.) -2, b.) 0, c.) 0, d.) 0 *

• 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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