SITE-C teams: Lesson 25
Use theCASIO CFX-9850G to find the area of the region bounded between the functions:
f(x) = 11 - x2
g(x) = x2 - 4 x + 5
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 11 - X2 and press EXE to store it in memory.
Enter into the Y2 slot the expression X2 - 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:
ò -1 11 - x2 dx - ò -1 x2 - 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 theCASIO CFX-9850G by pressing SHIFT AC/ON (OFF)