### Definite Integrals

Graphs the area under a function over an interval, and computes the
area using the antiderivative of the function.

How to use
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Examples
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Other Notes

**How to use**

- Enter the function
*f* (*x*) in the text
input field marked "*f* (*x*)=".
(Example:
*f* (*x*)=*x*^{2}-1)
- 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*)="
(Example:
*F* (*x*)=*x*^{3}/3-*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.
(Example:
[*a*,*b*]=[0,2])
- To erase the graph and all input fields, click the
"Clear" button

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.
For assistance checking the antiderivative *F* (*x*), try
computing its derivative *F* '(*x*) and checking
*F* '(*x*)=*f* (*x*) using
the Derivative Calculator.

**Examples**

**Other Notes**

The
graph shows *f*(*x*), with the area under the curve on the interval
[*a*,*b*] shaded so that positive areas are
blue
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*
red area).