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Evaluate a Definite Integral with the TI-84 Plus

You can use your TI-84 Plus calculator to evaluate a definite integral, which gives the area between the curve and the x-axis. For example, if f(x) is positive for

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

image1.jpg

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

  3. Press [7] to select the following option:

    image2.jpg
  4. If necessary, repeatedly press the up- and down-arrow keys until the appropriate function appears in the border at the top of the screen.

    This process is illustrated in the first screen.

    image3.jpg
  5. 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 Step 4. The number you key in appears after X=. This is illustrated in the second screen. If you make a mistake when entering your number, press [CLEAR] and re-enter the number.

  6. Press [ENTER].

    After pressing [ENTER], a Left Bound indicator (the dotted line with a triangular indicator) appears on the graphing screen.

  7. Enter the value of the Upper Limit b and press [ENTER].

    After pressing [ENTER], the value of the definite integral appears in the border at the bottom of the screen and the area between the curve and the x-axis will be shaded. This is illustrated in the third screen. The TI-84 Plus C uses interval notation to display the interval of the definite integral.

The shading of the graph produced by using the

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

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