The Fundamental Theorem of Calculus
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If is a continuous function on and is an antiderivative for on , then If we take and for convenience, then is the area under the graph of from to and is the derivative (slope) of . In the image above, the purple curve is —you have three choices—and the blue curve is .
Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA
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"The Fundamental Theorem of Calculus"
http://demonstrations.wolfram.com/TheFundamentalTheoremOfCalculus/
Wolfram Demonstrations Project
Published: March 7 2011