SITE-C teams: Lesson 23

Consider the function: f(x) = x2 - 5 x - 6

What is the area under this function and above the x-axis?

Turn on the CASIO CFX-9850G by pressing AC/ON.

Use the cursor arrows to highlight the GRAPH menu and press EXE or just press 5 when at the main menu screen.

In the Y1 slot enter X2 - 5 X - 6 and press EXE to store it in memory.

Press SHIFT F3 (V-Window) F1 (INIT) and set the y-parameters as follows:

 Ymin = -31 Ymax = 31 Yscale = 5

Press EXIT to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press F6 (DRAW) to see the graph.

To find the roots press SHIFT F5 (G-Solv) F1 (ROOT). The first root is x = -1. Press the right cursor arrow to obtain the second root. It is x = 6.

To find the area between the x-axis and the curve press SHIFT F5 (G-Solv) F6 ( |> ) F3 (ò dx) Use the right cursor arrow to move the cross hairs to ( -1, 0 ) and press EXE marking the lower bound of integration. Use the right cursor arrow again to move the cross hairs to ( 6, 0 ) and press EXE to mark the upper bound of integration and to calculate the numerical integral. It is -57.16666666667. The negative sign of the result is a consequence of the fact that the region lies entirely below the x-axis. The absolute value of the result is the required area.

Press EXIT and use the up or down cursor arrow to highlight Y1. Press F1 (SEL) to de-select it.

What is the value of ò -22 4 x - x3?

Use the cursor arrows to move to slot Y2 and enter 4 X - X^3 and press EXE.

Press SHIFT F3 (V-Window) F1 (INIT) EXIT.

Press F6 (DRAW) to see the graph of the function.

Press SHIFT F5 (G-Solv) F6 ( |> ) F3 (ò dx). Use the right cursor arrow to move the cross hairs to ( -2, 0 ) and press EXE marking the lower bound of integration. Use the right cursor arrow again to move the cross hairs to ( 2, 0 ) and press EXE to mark the upper bound of integration and to calculate the numerical integral. It is 0. This does not imply that the region involved has no area. Rather, because of the symmetry of the curve, the area of the part below the x-axis is precisely equal to that of the part above the x-axis. The area is 4.