Section 5.2. Read through the end of Example 1. Answer the following questions. Send an e-mail with subject line MA251 to email@example.com .
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 ________ ;"
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
The greatest integer function is integrable
on [0,5] because this function has a finite number of jump
discontinuities on this interval.