Lesson #129 Integrals involving Quadratics


Quote of the Day:
"God grant me the serenity to accept the things I cannot 
   change, the courage to change the things I can, and the 
   wisdom to know the difference."  -- Reinhold Niebuhr

Objectives:
The student will integrate integrals involving quadratics.
The student will complete the square.

1. Collect homework.

2. Review the concept of "Completing the Square."
      To complete the square:
        (1) If the coefficient of the squared term is one:
        (2) Divide the linear term by 2 and square it.
        (3) Add and subtract this amount to the expression.

        (1) If the coefficient of the squared term is not 
            one:  
            Factor out any coefficient of the squared term.
        (2) Divide the linear term by 2 and square it.
        (3) Inside the parentheses, add this amount.
            Outside the parentheses, subtract this amount 
            times the number which you factored out of the
            leading coefficient.

      Examples:

       

      Rewrite each of the following expressions in the form 
      of a perfect square and a constant:

       

3. If an integral involves a quadratic, you can complete 
   the square to get an integral that contains the sum or 
   difference of two squares.  Then use the method of trig 
   substitution.

4. Examples:     
       

5. Assignment:
      p. 535 (33, 34, 37, 38)
Lesson #129 Integrals involving Trig Quadratics

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