SITE-C teams: Lesson 27

 

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) = - 1/3 x + 4

g(x) = - x + 8

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 - ( 1 ¸ 3 ) X + 4 and press EXE to store it in memory.

Enter into the Y2 slot the expression - X + 8 and press EXE to store it in memory.

Press SHIFT F3 (V-Window), and set the parameters to:

Xmin = -2.7

Ymin = -2

Xmax = 9.9

Ymax = 6.2

Xscale = 1

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. This is ( 6, 2).

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 ( 8, 0 ).

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

6 8

ò 0 - 1/3 x + 4 dx + ò 6 - x + 8 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, 6 )

+ OPTN F4 (CALC) F4 (ò dx) VARS F4 (GRPH) F1 (Y2) , 6, 8 )

These keystrokes will cause the following to appear on the screen

ò (Y1, 0, 6 ) + ò (Y2, 6, 8 )

Press EXE and the area of the region will appear; the result is 20 square units.

Press EXIT. Press MENU.

Turn off the CASIO CFX-9850G by pressing SHIFT AC/ON (OFF)