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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
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.
- Spring '11