SITE-C teams: Lesson 25

Use the CASIO CFX-9850G to find the area of the region bounded between the functions:

f(x) = 11 - x^{2}

g(x) = x^{2} - 4 x + 5

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.

Enter into the Y1 slot the expression 11 - X^{2} and press **EXE** to store it in memory.

Enter into the Y2 slot the expression X^{2} - 4 X + 5 and press **EXE** to store it in memory.

Press **SHIFT** **F3** (V-Window) to enter the viewing window screen, and set the parameters to:

Xmin = -3.15 Ymin = -5 |
Xmax = 3.15 Ymax = 15.5 |
Xscale = 0.5 Yscale = 2 |

Press **EXIT** to return to the function list, and press **F6** (DRAW) to see the graph.

Press **SHIFT** **F5** (G-Solv) **F5** (ISCT) to find the first point of intersection of the two functions. This is (-1, 10). Press the right cursor arrow once to find the second point of intersection. This is (3, 2).

The area bounded by the two functions can be expressed mathematically by the following:

_{3} _{3}

ò
_{-1 } 11 - x^{2} dx - ò
_{-1} x^{2} - 4 x + 5 dx

where the bounds of integration were determined by the x-values of the points of intersection of the functions.

To numerically compute the value of the area in this region press **EXIT** **MENU** **1** to access the RUN menu.

Press **OPTN** **F4** (CALC) **F4** (ò
dx) **VARS** **F4** (GRPH) **F1** (Y1) **, - 1, 3 )**

**-** **OPTN** **F4** (CALC) **F4** (ò
dx) **VARS** **F4** (GRPH) **F1** (Y2) **, -1, 3 )**

These keystrokes will cause the following to appear on the screen

ò (Y1, -1, 3 ) - ò (Y2, -1, 3 )

Press **EXE** and the area of the region will appear; the result is 21.33333333 or 21 ^{1}/_{3} square units.

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

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