TheDefiniteIntegral - Define the definite integral....

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Unformatted text preview: Define the definite integral. explain all of your notation. Give a complete definition. Be sure to Let f (x) be a continuous function defined on the closed interval [a, b] . For each partition P of [a, b] of the form a = x0 ≤ x1 ≤ · · · ≤ xn = b , let Mi be the maximum value of f (x) on the subinterval [xi−1 , xi ] and let mi be the minimum value of f (x) on [xi−1 , xi ] . If there is exactly one number with n n Mi (xi − xi−1 ), mi (xi − xi−1 ) ≤ this number ≤ i=1 i=1 as P varies over all partitions of [a, b] , then this number is called the definite b integral of f on [a, b] and this number is denoted a f (x)dx . ...
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This note was uploaded on 10/12/2011 for the course MATH 142 taught by Professor Kustin during the Spring '11 term at South Carolina.

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