Evaluate a Definite Integral with the TI-84 Plus

You can use the option on the Calculate menu of the TI84 graphing calculator to find the value of a definite integral of a function. If f(x) is positive for

and then the definite integral

also gives the area between the curve and the x-axis for

To evaluate the definite integral, perform the following steps:

1. Graph the function f(x) in a viewing window that contains the lower limit a and the upper limit b.

   To get a viewing window containing a and b, these values must be between Xmin and Xmax.

2. Set the Format menu to ExprOn and CoordOn.

3. Press [2nd][TRACE] to access the Calculate menu.

4. Press [7] to select the

   

   option.

5. If necessary, repeatedly press

   

   until the appropriate function appears at the top of the screen.

   This process is illustrated in the first graph in the following figure.

6. Enter the value of the lower limit a.

   To do so, use the keypad to enter the value of the lower limit a. As you use the keypad, X= appears, replacing the coordinates of the cursor location appearing at the bottom of the screen in the previous step. The number you key in appears after X=. This is illustrated in the second graph in the figure. If you make a mistake when entering your number, press [CLEAR] and re-enter the number.

7. Press [ENTER].

   After pressing [ENTER], a left bound indicator appears at the top of the screen.

8. Enter the value of the upper limit b and press [ENTER].

   After pressing [ENTER], the value of the definite integral appears at the bottom of the screen and the area between the curve and the x-axis, for

   

   will be shaded. This is illustrated in the third graph in the following figure.

   

The shading of the graph produced by using the

option on the Calculate menu does not automatically vanish when you use another Calculate option. To erase the shading, press [2nd][PRGM][1] to invoke the ClrDraw command on the Draw menu. The graph is then redrawn without the shading.