SITE-C teams: Lesson 27
Use theCASIO 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 theCASIO 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:
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 theCASIO CFX-9850G by pressing SHIFT AC/ON (OFF)