13112an5.6-8

# 13112an5.6-8 - c Kendra Kilmer March 1 2012 Section 5.3...

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c c Kendra Kilmer March 1, 2012 Section 5.3 - Evaluating Definite Integrals Evaluation Theorem If f is a continuous function on [ a , b ] , and F is any antiderivative of f , then Example 1: Evaluate the following: a) i 3 2 ( x 2 + 4 ) dx b) i 4 0 ( 4 t + t ) dt c) i 5 1 ( e x + cos x ) dx d) i 2 0 ( 2 x + 3 ) 2 dx 6

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c c Kendra Kilmer March 1, 2012 Indefinite Integrals The notation i f ( x ) dx is traditionally used for a general antiderivative of f and is called an indefinite integral . Thus, i f ( x ) dx = F ( x ) means F ( x ) = f ( x ) Note: We connect the two types of integrals by the Evaluation Theorem, i b a f ( x ) dx = p i f ( x ) dx Pb b a = F ( b ) F ( a ) Table of Indefinite Integrals i [ f ( x ) ± g ( x )] dx = i f ( x ) dx ± i g ( x ) dx i cf ( x ) dx = c i f ( x ) dx i x n dx = x n + 1 n + 1 + C ( n n = 1 ) i 1 x dx = ln | x | + C i e x dx = e x + C i a x dx = a x ln a + C i sin xdx = cos x + C i cos xdx = sin x + C i sec 2 xdx = tan x + C i
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## This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.

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13112an5.6-8 - c Kendra Kilmer March 1 2012 Section 5.3...

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