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