First Fundamental Theorem of Calculus
المؤلف:
Anton, H.
المصدر:
"The First Fundamental Theorem of Calculus."
الجزء والصفحة:
...
15-5-2018
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First Fundamental Theorem of Calculus
The first fundamental theorem of calculus states that, if 
is continuous on the closed interval ![[a,b]](http://mathworld.wolfram.com/images/equations/FirstFundamentalTheoremofCalculus/Inline2.gif)
and 
is the indefinite integral of 
on ![[a,b]](http://mathworld.wolfram.com/images/equations/FirstFundamentalTheoremofCalculus/Inline5.gif)
, then
This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral.
REFERENCES:
Anton, H. "The First Fundamental Theorem of Calculus." §5.8 Calculus: A New Horizon, 6th ed. New York: Wiley, pp. 326-335, 1999.
Apostol, T. M. "The Derivative of an Indefinite Integral. The First Fundamental Theorem of Calculus." §5.1 in Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, pp. 202-204, 1967.
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