SITE-C teams: Lesson 26

Use the CASIO CFX-9850G to find the area of the region bounded in the first quadrant of the xy-plane between the functions:

f(x) = - 0.75 x + 6

g(x) = - 3 x + 15

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 - 0.75 X + 6** **and press

Enter into the Y2 slot the expression - 3 X + 15 and press **EXE** to store it in memory.

Press **SHIFT** **F3** (V-Window) **F1** (INIT), and set the y parameters to:

Ymin = -2 |
Ymax = 6.2 |
Yscale = 1 |

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 point of intersection of the two functions. This is ( 4, 3).

Press **SHIFT** **F5** (G-Solv) **F1** (ROOT) to find the where Y2 crosses the x-axis use the down cursor arrow to activate Y2 and press EXE. The root is ( 5, 0 ).

The area in the first quadrant of the xy-plane bounded by the two functions can be expressed mathematically by the following:

_{4} _{5}

ò
_{0 } - 0.75 x + 6** **dx + ò

where the bounds of integration were determined by the x-value of the point of intersection of the functions and the root of Y2. 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) **, 0, 4 )**

**+** **OPTN** **F4** (CALC) **F4** (ò
dx) **VARS** **F4** (GRPH) **F1** (Y2) **, 4, 5 )**

These keystrokes will cause the following to appear on the screen

ò (Y1, 0, 4 ) + ò (Y2, 4, 5 )

Press **EXE** and the area of the region will appear; the result is 19.5 or 19 ^{1}/_{2} square units.

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

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