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 STANDARD 3.2A2 The definite integral of a continuous function f over the interval [a,b], denoted by ʃ f(x)dx, is the limit of Riemann sums as the widths of the subintervals approach 0.  That is, over the interval [a,b], denoted by ʃ f(x)dx=lim, as max Δxi approaches 0, Σf(xi)Δxi, from i=1 to n, where xi is a value in the ith subinterval, Δxi is the width of the ith subinterval, n is the number of subintervals, and max Δxi is the width of the largest subinterval.  Another form of the definition is over the interval [a,b], ʃ f(x)dx=lim, as n approaches ∞, Σf(xi*)Δxi, from i=1 to n, where Δxi=(b-a)/n and xi* is a value in the ith subinterval.

 To access Practice Worksheets aligned to the College Board's AP Calculus Curriculum Framework, click on the Essential Knowledge Standard below.  To see the text of an EKS, hover your pointer over the Standard. LIMITS 1.1A1 1.1A2 1.1A3 1.1C2 1.1C3 1.2A2 1.2A3 DERIVATIVES 2.1A1 2.1A2 2.1A3 2.1C1 2.1C2 2.1C3 2.1C4 2.1C5 2.1C6 2.1D1 2.2A1 2.2A2 2.2A3 2.3A2 2.3B1 2.3B2 2.3C1 2.3C2 2.3C3 2.3F1 2.4A1 INTEGRALS 3.2A1 3.2B2 3.3B1 3.3B2 3.3B3 3.3B5 3.4B1 3.4C1 3.4D1 3.4D2 3.5A1 3.5A2 3.5A3 SERIES 4.1A2 COMPLETE JMAP FOR CALCULUS

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