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Exploring Area between Curves

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Harumi Monroy
Jonathan Sahagun

xMin =
xMax =
yMin =
yMax =

From X1 =
To X2 =

Recangles # =
Method =

First Function f(x) =
Second Function f(x) =


Suggestions for Using the JavaScript Graph
All viewers will join the National Curve Bank - A MATH Archive in thanking Harumi Monroy of CS 491, for developing this material.  The relevant mathematics on Areas between Curves was uploaded over the Fall of 2006. Check back later for more practice.

Calculus texts have problems on finding the Areas between Curves in the chapters on applications of Integration.  The NCB suggests finding some of these examples in a text and trying them in Harumi's graph.  This practice is often helpful.

"Sometimes it's difficult, or even impossible, to find the points of intersection of two curves exactly....We can use a graphing calculator or computer to find approximate values for the intersection points and then proceed as before."
James Stewart, Calculus, 5th ed, Thomson: Brooks/Cole, 2003, p. 377.

Experimenting on a computer with the approximation for finding the area using rectangles is fascinating.  As the number of rectangles increases, the approximation improves.  Therefore, mathematicians define the
area A between the two curves as the limit of the sum of the areas of these approximating rectangles where n is the number of rectangles bounded between a and b.
Equations:  Area between curves

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JAVA applet contributed by
Harumi Monroy

Java Script update contributed by
Jonathan Sahagun