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 AC/ON.

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 EXE to store it in memory.

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 4 - 3 X + 15 dx

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.