lecture2_1_13.pdf

# lecture2_1_13.pdf - Outline Introduction Integral...

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Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 1 The Fundamental Calculus Theorem, Part 1 Theorem Assume that f ( x ) is continuous on [ a , b ] . If F ( x ) is an antiderivative of f ( x ) on [ a , b ] then b a f ( x ) dx = F ( b ) F ( a ) . Dr. Vasileios Maroulas Assistant Professor Department of Mathematics University of Tennessee [email protected] Calculus II-Math 142

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Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 2 Theorem Assume that f ( x ) is continuous on an open interval I and let a I. Then the area function A ( x ) = x a f ( t ) dt is an antiderivative of f ( x ) on I, i.e. A ( x ) = f ( x ) . Equivalently, d dx x a f ( t ) dt = f ( x ) . Furthermore, A ( x ) satisfies the initial condition A ( a ) = 0 . Dr. Vasileios Maroulas Assistant Professor Department of Mathematics University of Tennessee [email protected] Calculus II-Math 142
Outline Introduction Integral Applications I Techniques Applications II Infinite series The Fundamental Calculus Theorem, Part 2 Dr. Vasileios Maroulas

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• Fall '19
• Calculus, Indian mathematics, Express f, Dr. Vasileios Maroulas

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