Area Function for a Piecewise Curve
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Adjust the values for 
and 
to see the area between the piecewise curve and the -axis over the interval [, ]. Check the box to see the graph of the area as a function of , and observe the effect of changing the value of .
Contributed by: Charles E. Oelsner (Manlius Pebble Hill School) (March 2011)
Open content licensed under CC BY-NC-SA
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Details
This demonstrates that for a fixed value of , the area between a curve and the -axis over [, ] is a function of . It is then natural to consider the derivative of this area function, which motivates one part of the fundamental theorem of calculus. Note that the area function is smooth, while its derivative, the piecewise-defined curve, is not.
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