Section 5.2.  Read from the end of Example 1 on page 374 through the end of the section.  Pay particular attention to Example 4, the Properties of the Integral (on pages 379 and 381), and Equation 5. Answer the following questions.  Send an e-mail with subject line MA251 to .

1)  What is the value of (sum from k=1 to 7) 4, that is,           ?

7 x 4 = 28

2) In the midpoint rule, Delta x is defined as (b-a)/n.  In your own words, what is (b-a)/n?

This is the width of one of the rectangles into which we use to approximate the area being calculated; equivalently, this value is the length of one of the subintervals into which we divide the interval on the x-axis from a to b. 

3) If        and          , then what is            ?  That is, if the definite integral from 0 to 10 of f(x) dx is 11 and the definite integral from 0 to 8 of f(x) dx is 7, then what is the definite integral from 8 to 10 of f(x) dx ?

11 - 7 = 4