How to Find the Area of a Region Using a Graphing Calculator

by Nucreisha Langdon

Graphing calculators are capable of many operations besides the obvious feature of drawing graphs. Scientists, mathematicians and students can also use graphing calculators to solve equations and compute numerical values of derivatives and integrals. In calculus, the integral of a function allows you to find the area of the region under the function's curve and above the x-axis, as well as the region between two curves. While it is possible to solve some types of integrals by hand, you will find graphing calculators to be more convenient in practical applications.

Press the "Math" button and select "fnInt(" from the menu. The word "fnInt(" will appear on your calculator's screen with the cursor blinking after the parenthesis.

Enter the equation of the function that bounds the region whose area you wish to calculate, then type a comma. For example, if you are computing the area under the function f(x) = x^2 that lies above the x-axis, you type "x^2," after the parenthesis. If you are computing the area of a region bounded by two curves, enter the equation of the top curve, then type a minus sign and then type the equation bottom curve followed by a comma. For example, if you wish to calculate the area between x^2 and x/4, you type "x^2-x/4," after the parenthesis.

Type "x" followed by a comma. Your calculator now reads "fnInt(x^2,x," on the screen.

Type the lower x-bound of the region followed by a comma. For instance, if the region spans the interval from 3 to 7, the lower bound is 3. Your graphing calculator will show "fnInt(x^2,x,3," on the screen.

Enter the upper x-bound of the region followed by a closing parenthesis. For instance, if the upper bound is 7 your calculator will display "fnInt(x^2,x,3,7)" on the screen.

Press the "Enter" key to evaluate the integral. After one or two seconds, the calculator will display the area of the region under the curve.

Things You Will Need

  • Graphing calculator

About the Author

Nucreisha Langdon has written professionally since 1991. She has ghostwritten more than 20 romantic fantasy novels, while her nonfiction work has appeared in the "Gainesville Sun" and the "Austin Chronicle." Langdon holds a Bachelor of Science in mathematics and a Bachelor of Arts in English from the University of Florida.

Photo Credits

  • Jupiterimages, Brand X Pictures/Brand X Pictures/Getty Images