JMAP accepts donations online

JMAP


Search www.jmap.org:

RESOURCES BY STANDARD
AI  GEO  AII  PLUS
or
www.commoncorestatestandards.org
and
CALCULUS

RESOURCES BY TOPIC
AI  GEO  AII  PRECALCULUS
CALCULUS

QUICK TOPICS

REGENTS EXAMS

WORKSHEETS

REGENTS BOOKS

WORKSHEET GENERATORS

EXTRAS

REGENTS EXAM ARCHIVES
1866-2017

JMAP RESOURCE ARCHIVES
AI/GEO/AII (2015-17)
IA/GE/A2 (2007-17)
Math A/B (1998-2010)

REGENTS RESOURCES

INTERDISCIPLINARY EXAMS

NYC TEACHER RESOURCES

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(xixi, 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

 

 
HOME REGENTS REVIEW DONORS
ABOUT JMAP ROSTER DONATE
Questions should be directed to JMAP's Editor, Steve Sibol or Cofounder, Steve Watson
Copyright 2017  JMAP, Inc. - All rights reserved
JMAP, Inc. is a 501(c)(3) New York Not-for-Profit Corporation