Graphs the area under a function over an interval, and computes the
area using the antiderivative of the function.
How to use
How to use
The text input fields for f (x) and F (x)
can accept a wide variety of expressions
to represent functions, and the
buttons under the graph
allow various manipulations of
the graph coordinates.
The text input fields for a and b can accept real numbers
in decimal notation.
- Enter the function f (x) in the text
input field marked "f (x)=".
- Click the "Graph" button
(this button also refreshes the graph)
- Enter the antiderivative F (x)
(so that F '(x)=f (x)) in the text input
field marked "F (x)="
- Enter the endpoints of the interval [a,b]
for the definite integral in the text input fields marked
"a=" and "b=",
and click the "Graph" button to refresh.
- To erase the graph and all input fields, click the
For assistance checking the antiderivative F (x), try
computing its derivative F '(x) and checking
F '(x)=f (x) using
the Derivative Calculator.
graph shows f(x), with the area under the curve on the interval
[a,b] shaded so that positive areas are
and negative areas are red.
A label under the graph shows the net area under the graph.
In the "Polynomial" example above,
part of the shaded area is above the x-axis
(in blue) and part below it
(in red). The area above the axis is a bit
larger than the area below it, giving a positive value for net area
(blue area minus