CPM Homework Help : APCALC Problem 2-28

Write an equation that will approximate the area under $f (x) = \cos(x)$ over the interval $[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } ]$ using six trapezoids with equal height. How can you use the fact that this is an even function to save yourself some work?

Hint:

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:

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

More Help:

Notice the symmetry about the $y$ -axis. If we evaluate the trapezoidal sum on one side of the $y$ -axis, can we determine the trapezoidal sum on the other side of the $y$ -axis?