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lecture1_28_13.pdf - Outline Introduction Integral...

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Outline Introduction Integral Applications I Techniques Applications II Infinite series The Definite Integral Theorem Assume that the functions f , g below are integrable over the intervals that the integral is considered: For any constant C: b a Cdx = C ( b a ) . b a f ( x ) + g ( x ) dx = b a f ( x ) dx + b a g ( x ) dx b a Cf ( x ) dx = C b a f ( x ) dx b a f ( x ) dx = a b f ( x ) dx a a f ( x ) dx = 0 c a f ( x ) dx = b a f ( x ) dx + c b f ( x ) dx, for a b c. If f ( x ) g ( x ) for x in [ a , b ] , then b a f ( x ) dx b a g ( x ) dx 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 Definite Integral Example Show that for all b : b 0 xdx = b 2 2 . 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 Definite Integral Example Calculate 7 4 xdx . Dr. Vasileios Maroulas Assistant Professor Department of Mathematics University of Tennessee
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  • Fall '19
  • Calculus, assistant professor, Indian mathematics, Department of Mathematics University of Tennessee, Dr. Vasileios Maroulas

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