Graphs a function f(x) and the area under the graph of
f (x)
for a given interval, and finds approximations to that area by
the Trapezoid Rule and Simpson's Rule.
Enter the function f (x) in the text
input field
marked "f (x)="
(Example:
f (x)=4-x^{2})
Click the "Graph" button
(this button also refreshes the graph)
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]=[-2,2])
For each method, the
"+" and "-"
buttons under the label marked "n=" change the
number of subintervals used for that method
(Example:
n=20 for both methods)
To erase the graph and all input fields, setting the
"n=" fields to default values, click the
"Clear" button
The text input field for 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.
Examples
Polynomial: f (x)=4-x^{2}
[a,b]=[-2,2] n=20 for both
Exponential: f (x)=e^{2}
[a,b]=[0,2] n=10 for both
Trigonometric: f (x) = sin x
[a,b]=[0,3.14159] n=10 for both
Other Notes
The area under the curve on the interval
[a,b] shaded so that positive areas are
blue
and negative areas are red.
The approximate area computed
by each method is shown in the labels marked "Area=".