Quote of the Day:
"Nothing was ever achieved without enthusiasm." – Emerson

Objectives:
The student will integrate integrals involving sums and 
   differences of squares.

1. Collect homework.

2. Recall:

3.  Given two sides of a right triangle, a and u,
    what are the three possibilities that exist?
    Draw the triangles and label the third side in each.

    We will use these three triangles any time that we have 
    an integral involving the sum or difference of two 
    squares.  We will use the letter a to represent 
    constants and the letter u to represent variables.
    
    This requires no memorization, since you just set up 
    the triangle so that the third side corresponds to 
    what you are looking for (a2 - u2, u2 - a2, or a2 + u2). 
    Here is how you use the triangle:

   What we are doing is taking an integral involving 
   the sum or the difference of two squares which we
   can not integrate (because it is in the denominator or 
   because it is under a square root), and making an 
   appropriate trigonometric substitution so that we obtain 
   an integral of just one term.  We can then integrate it 
   or take its square root.


4. Examples:

5. Assignment:
     p. 535 (1, 4, 5)  

Click here to go to the next page