Section5_2_review

Section5_2_review - Section 5.2: The Definite Integral x...

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Section 5.2: The Definite Integral The approximation for area, A , of a region S that is bounded by a curve y = f x (29 and the x -axis as x goes from a to b developed in Section 5.1 improves as n , the number of subintervals, increases until it becomes exact: A = lim n →∞ f x i * ( 29 x i = 1 n and any choice of sample point gives the same answer. This expression defines the definite integral of a continuous function f x ( 29 on a , b [ ] : A = f x (29 dx = a b lim n →∞ f x i * (29 x i = 1 n . If f x (29 0 over a , b [ ] , then the definite integral is the total area bounded by the curve y = f x (29 and the x -axis as x goes from a to b . If y = f x (29 takes on both positive and negative values over a , b [ ] , then the definite integral is the net area (area of the region above the x -axis minus the area of the region below the x -axis) bounded by the curve y = f x (29 and the x -axis as x goes from a to b . In this section, we evaluate the right-hand side of the definition of the definite integral
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.

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Section5_2_review - Section 5.2: The Definite Integral x...

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