Evaluate a Definite Integral on the TI-83 Plus

You can use the TI-83 Plus graphing calculator to evaluate a definite integral. For example, if the function f(x) is positive for the following value


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



  5. If necessary, repeatedly press


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

  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=. 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.

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.

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