Copy and paste: If you adjust the width and height parameters, the graph will scale to fit inside the box.
-- Polynomial coefficients (a
-- A polynomial equation can be specified in the url by passing the coefficients (a) as a reversed, comma delimited sequence. For example: the equation:
y = x
2 + 2 x - 3
Is referenced as:
-- the coordinates of points on the graph.
-- A series of points can be entered as a comma separated list of x, y coordinates. For example, the points:
(3,7), (2,-3), and (5,1)
Can be plotted as:
-- Show the input box to add lines and points to the graph.
none - Turn off the input boxes at the top of the graph:
polynomial - (default) Show the interface for polynomial equations.
points - Show the interface for adding points to the graph.
For example, the url for the above equation with no input box would be:
-- Adjust the size of the graph in the iframe. Options:
auto - (default) scales so graph is slightly smaller than window so there are no scroll bars on the frame.
full - scales so graph is fully fits the smallest dimension of the iframe window.
none - creates 600x600 pixel graph in a window.
For example, the url for the above equation with no input box and full fit:
-- The maximum range (positive and negative) for the axes.
-- The default range is
10 so the x and y axes minimums are -10 and the maximums are 10 (as shown above). By default, the tick marks are interpolated to be 10% of the range. To change the range to 20 use:
So, for example:
-- The interval between tick marks on the axes
-- The default tick marks are interpolated to be 10% of the range if the width of the graph is greater than 300 pixels, and 20% if smaller (note that these do not exactly correspond to the values set for the iframe since, except for the
fit=none option, some adjustment is made. To change the dx to 5 use:
So, for example (with the range set to 20):
-- Find the area under the curve within the given bounds.
-- Enter a comma delimited list of:
a - the left bound (lower limit) of the area.
b - the right bound (upper limit) of the area.
n - the number of trapezoids used in the integration.
Numerical integration of the function
f(x) = -0.25x between the limits 2 + x + 4 a = 1 and b = 4 using four trapezoids ( n = 4).
So, to find the integral (area under the curve) between
x = 1 and x = 5 using 4 trapezoids use:
For an example, we'll find this integral for the curve
f(x) = -0.25x:
2 + x + 4
The area using 4 trapezoids is 17.5 as shown in this
numerical integration example.