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

selliott@utm.edu .

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