SITE-C teams: Lesson 23

Consider the function: f(x) = x^{2} - 5 x - 6

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

Turn on the **CASIO CFX-9850G** by pressing

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 X^{2} - 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
_{-2}^{2} 4 x - x^{3}?

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

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.

Press **EXIT** **MENU**.

Turn off the **CASIO CFX-9850G** by pressing