A function $f$ is continuous over the interval $[2, 8]$ and has values that are given in the table at right.

1. Using the sub-intervals $[2, 5], [5, 7]$, and $[7, 8]$, what is the trapezoidal approximation of $\int _ { 2 } ^ { 8 } f ( x ) d x$?

   Hint (a):

   The Trapezoid Rule

   The Trapezoid Rule can be used to approximate the area under a curve if the widths, $\Delta x$, of all trapezoids are of equal size:

   $\left. \begin{array} { r } { A = \frac { \Delta x } { 2 } ( f ( a ) + 2 f ( a + \Delta x ) + 2 f ( a + 2 \Delta x ) + \ldots } \\ { + 2 f ( b - \Delta x ) + f ( b ) ) } \end{array} \right.$

2. Over which sub-interval is the average slope a minimum?

   1. $[2, 5]$ 

   2. $[5, 7]$ 

   3. $[7, 8]$