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

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
_{-1}^{1} 1 / (x^{3} + 1 ) ?

Use the cursor arrows to move to slot Y2 and enter 1 / ( X^{2} + 1 )** ** and press

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
_{0}^{1} 1 / (x^{3} + 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.

Press **EXIT** **MENU**.

Turn off the **CASIO CFX-9850G** by pressing