SITE-C teams: Lesson 24

Consider the function: f(x) = cos ( x / 2 )

What is the area under this function and above the x-axis between -p and p ?

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.

In the Y1 slot enter cos ( X ¸ 2) and press EXE to store it in memory.

Press SHIFT F3 (V-Window) F2 (TRIG).

Press EXIT to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press F6 (DRAW) to see the graph.

To find the area between the x-axis and the curve from - p to p , press SHIFT F5 (G-Solv) F6 ( |> ) F3 (ò dx), use the right cursor arrow to move the cross hairs to ( -3.1415926535, -1.E-13 ) and press EXE marking the lower bound of integration. Use the right cursor arrow again to move the cross hairs to ( 3.1415926535, -1.E-13 ) and press EXE to mark the upper bound of integration and to calculate the numerical integral. It is 4.

Press EXIT and use the up or down cursor arrow to highlight Y1. Press F1 (SEL) to de-select it.

What is the value of ò -11 1 / (x3 + 1 ) ?

Use the cursor arrows to move to slot Y2 and enter 1 / ( X2 + 1 ) and press EXE.

Press SHIFT F3 (V-Window) F1 (INIT) EXIT.

Press F6 (DRAW) to see the graph of the function.

Press SHIFT F5 (G-Solv) F6 ( |> ) F3 (ò dx). Use the right cursor arrow to move the cross hairs to ( -1, 0.5 ) and press EXE marking the lower bound of integration. Use the right cursor arrow again to move the cross hairs to ( 1, 0.5 ) and press EXE to mark the upper bound of integration and to calculate the numerical integral. It is 1.57079633. Press EXIT.

Is the area symmetrically distributed? What is the value of ò 01 1 / (x3 + 1 ) ?

Press F6 (DRAW) SHIFT F5 (G-Solv) F6 ( |> ) F3 (ò dx). Use the right cursor arrow to move the cross hairs to ( 0, 1 ) and press EXE marking the lower bound of integration. Use the right cursor arrow again to move the cross hairs to ( 1, 0.5 ) and press EXE to mark the upper bound of integration and to calculate the numerical integral. It is 0.78539816. So, yes it is.