Graphs a function f
) and approximations to the area under
the graph of
for a given interval, using sums of areas of rectangles with the heights
of the rectangles determined by f
How to use
How to use
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.
- Enter the function f (x) in the text
marked "f (x)="
- 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
- Use the "+" and "-"
buttons under the label marked "n="
to change the number of subintervals used for the approximation
- 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,
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
n=20 for both
n=10 for both
f (x) = sin x
n=6 for both
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=".