ReviewC5

ReviewC5 - Sections 5.1, 5.2, 5.3, 5.4 and 5.5: Review...

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Sections 5.1, 5.2, 5.3, 5.4 and 5.5: Review Theory Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 5.1 The Area Problem : Find the area of the region S that lies under the curve y = f ( x ) from a to b . First, we approximate the region S by n rectangles (using left endpoints, right endpoints or mid- points x * i ). Then we take the limit of the sum of the areas of these rectangles (Riemann sum) as we increase the number of rectangles. So, define the actual area A of the region S to be the limit of the Riemann sum: A = lim n →∞ Σ n i =1 f ( x * i ) 4 x = Z b a f ( x ) dx 5.2 Some Important Properties of the Definite Integral R b a f ( x ) dx = - R a b f ( x ) dx R a a f ( x ) dx = 0 R b a cf ( x ) dx = c R b a f ( x ) dx where c is any constant. R b a [ f ( x ) ± g ( x )] dx = R b a f ( x ) dx ± R b a g ( x ) dx R c a f ( x ) dx + R b c f ( x ) dx = R b a f ( x ) dx If f ( x ) 0 for a x b , then R b a f ( x ) dx 0. 5.3
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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ReviewC5 - Sections 5.1, 5.2, 5.3, 5.4 and 5.5: Review...

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