Section 5.2.  Read through the end of Example 1.  Answer the following questions.  Send an e-mail with subject line MA251 to selliott@utm.edu .

1) Fill in the blanks:  If a function f is integrable, then the limit in Definition ___ _____ , and we may choose the sample points xi* any way we like.  To simplify the calculation, we often use _______ _______ .  In this case, we get Theorem 4. 

2, exists, right, endpoints

2) Fill in the blank:  Note 2 says that "the definite integral . . . is a ________ ;"

number

3) After reading Theorem 3, explain why the greatest integer function f(x) = [[x]] is, or is not, integrable on [0,5].  (See Example 10 on page 105 if you have forgotten the greatest integer function).

The greatest integer function is integrable on [0,5] because this function has a finite number of jump discontinuities on this interval.