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

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A graphing calculator is a handy assistant to the budding mathematician. When the sides are curved, it can be difficult to find the area. Graphing calculators are a wonder for this math problem that can be most perplexing. A good graphing calculator is 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 available menu. The word "fnInt(" will appear on your calculator's screen with the cursor blinking after the parenthesis.

First Steps to Digit Deduction

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.

Further Calculations

Type "x" followed by a comma. Your calculator should now read "fnInt(x^2,x," on the display 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.

Final Steps

After completing the above step, enter the upper x-bound of the region followed by a closing parenthesis. This will give you a new equation. 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 in number format. For example, definite integrals are a simple way to describe the area that is under a curve. It can be an intriguing concept for mathematicians.


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.