Graphs a function f(x) and approximations to the area under
the graph of
f(x)
for a given interval, using sums of areas of rectangles with the heights
of the rectangles determined by f(x).
Enter the function f (x) in the text
input field
marked "f (x)="
(Example:
f (x)=4-x2)
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])
Use the "+" and "-"
buttons under the label marked "n="
to change the number of subintervals used for the approximation
(Example: n=8)
The slider determines which point in each subinterval is used to
determine the height of the rectangle, from left endpoint to right endpoint
(Example: left endpoint)
The "Left", "Mid", and
"Right" buttons specify left endpoint,
midpoint, and
right endpoint, respectively, and adjust the slider appropriately
To erase the graph and all input fields, setting the
slider to a default position and n to a default value, 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-x2
[a,b]=[-2,2] n=20 for both left|mid|right
Exponential: f (x)=e2
[a,b]=[0,2] n=10 for both left|mid|right
Trigonometric: f (x) = sin x
[a,b]=[0,3.14159] n=6 for both left|mid|right
Other Notes
The graph of f (x) is shown, with the rectangles
over subintervals of [a,b]
drawn in outline so that positive areas are green
and negative areas are red.
The approximate area computed is shown in the label marked "Area=".