Quote of the Day:
"It is clear that Economics, if it is to be a science at 
   all, must be a mathematical science ... simply because 
   it deals with quantities... 
   As the complete theory of almost every other science 
   involves the use of calculus, so we cannot have a true 
   theory of Economics without its aid." 
      -- W. S. Jevons

Objectives:
The student will learn the properties of the definite 
   integral and apply them when solving integrals. 

The student will learn the Fundamental Theorem of Calculus and apply it.

2. The Fundamental Theorem of Calculus 
      Each branch of mathematics has a fundamental theorem 
      associated with it.

      The Fundamental Theorem of Arithmetic:
        Any positive integer can be represented in exactly 
        one way as a product of primes.

      The Fundamental Theorem of Algebra:
        Every polynomial of degree n has exactly n zeroes. 

      The Fundamental Theorem of Geometry:
        No theorem wears this title, but perhaps the 
        Pythagorean Theorem deserves it.

      The Fundamental Theorem of Calculus – there are 
        actually two parts to this theorem:

        The First Fundamental Theorem of Calculus:
          The derivative of the integral of a function
            is equal to the function.
 
        The Second Fundamental Theorem of Calculus:
          The integral of the derivative of a function is  
            is equal to the function evaluated at its 
            endpoints.

   The F.T.C. tells us that we can evaluate a definite 
      integral by taking an indefinite integral and 
      substituting in the endpoints and taking the 
      difference:      

      Remember that you can't spell FUNDAMENTAL without FUN (and MENTAL, and DA).
      So, think of The Fundamental Theorem of Calculus as DA MENTAL FUN.

3. Examples:
       

4. Properties of the Definite Integral
       

5. Examples of the Properties of the Definite Integral
       

6. Compute the Definite Integral in this Comic Strip

7. Assignment
   p. 394 (15, 16, 19, 20, 21)              
   p. 406 (3, 6, 9, 11, 13)    

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