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How to Find the Area Between Graphs Using GeoGebra
You can use GeoGebra to find the area between two graphs.
There is a built-in command in GeoGebra that does it for you:
IntegralBetween(<Function>, <Function>, <Start x-Value>, <End x-Value>)
This command is sometimes problematic, however, because the integral between two functions can end up being negative. To avoid this, you can split the integral up at all the points of intersection, and make sure that the uppermost function is entered first in the command given above.
Below is another method that always returns the area you want, without having to split the integrals or change the order.
Note! In the instructions below, you’ll always get the correct area under the graph, but the area you actually see in the Graphics View may not be drawn between the graphs. GeoGebra usually moves it closer to the -axis, like in the picture below. This is because the part of the function that was supposed to be under the -axis is instead reflected by the -axis using the abs(x) function in Algebra View. In the instructions, we’ll also look at how to hide the drawn area.
GeoGebra Instruction 1
- 1.
- Open
Algebra ViewandGraphics Viewunder
Viewin
Menu. - 2.
- First, save your expressions. In order to do this you type
f(x) = first function
g(x) = second function
- 3.
- Use
Intersect
to find the intersections between the functions. - 4.
- Type
Integral(<Function>, <Start x-Value>, <End x-Value>)
in
CAS. Fill inabs(f(x) - g(x))for<Function>. For<Start x-Value>, type the -value of the leftmost point of intersection. For<End x-Value>, type the -value of the rightmost point of intersection. PressEnter.
