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Integration by parts

AP Calc Study Guide

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Calculus
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Calculus
Mathematical analysis
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Differentiation rules
Integral calculus
Integration by parts
Integration by substitution
Product rule
Natural logarithm
Quotient Rule
derivative
Differential equation
education

Copyright 1996,1997 Elaine Cheong All Rights Reserved Study Guide for the Advanced Placement Calculus AB Examination By Elaine Cheong 1 Table of Contents INTRODUCTION 2 TOPICS TO STUDY 3 ? Elementary Functions 3 ? Limits 5 ? Differential Calculus 7 ? Integral Calculus 12 SOME USEFUL FORMULAS 16 CALCULATOR TIPS AND PROGRAMS 17 BOOK REVIEW OF AVAILABLE STUDY GUIDES 19 ACKNOWLEDGEMENTS 19 2 Introduction Advanced Placement1 is a program of college-level courses and examinations that gives high school students the opportunity to receive advanced placement and/or credit in college. The Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus, covering a full-year college mathematics course.

Handbook

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Algebra
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Mathematical analysis
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Analytic functions
Integral calculus
Complex analysis
trigonometry
Exponentials
Hyperbolic function
Bessel function
Euler's formula
Integration by parts
Differential equation

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Bibliography; Physical Constants 1. Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Arithmetic and Geometric progressions; Convergence of series: the ratio test; Convergence of series: the comparison test; Binomial expansion; Taylor and Maclaurin Series; Power series with real variables; Integer series; Plane wave expansion

AP Calculus Cheat Sheet

Subject: 
Calculus
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Calculus
Mathematical analysis
Mathematics
Integral calculus
Differentiation rules
Integration by parts
Differential equation
derivative
Quotient Rule
Integration by substitution
Antiderivative
Product rule

Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. ? 2005 Paul Dawkins Limits Definitions Precise Definition : We say ( )limx a f x L? = if for every 0e > there is a 0d > such that whenever 0 x a d< - < then ( )f x L e- < . ?Working? Definition : We say ( )limx a f x L? = if we can make ( )f x as close to L as we want by taking x sufficiently close to a (on either side of a) without letting x a= . Right hand limit : ( )limx a f x L+? = . This has the same definition as the limit except it requires x a> . Left hand limit : ( )limx a f x L-? = . This has the same definition as the limit except it requires x a< . Limit at Infinity : We say ( )limx f x L?? = if we

Ch8 SG

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Calculus
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Integral calculus
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Tags: 
Calculus
Mathematical analysis
Mathematics
Integral calculus
Integration by parts
Natural logarithm
Hyperbolic function
Trigonometric substitution
Integration by substitution
derivative
Integral of secant cubed
Sum rule in integration

317 CHAPTER 8 Principles of Integral Evaluation EXERCISE SET 8.1 1. u = 3? 2x, du = ?2dx, ? 1 2 ? u3 du = ?1 8 u4 + C = ?1 8 (3? 2x)4 + C 2. u = 4 + 9x, du = 9dx, 1 9 ? u1/2 du = 2 3 ? 9u 3/2 + C = 2 27 (4 + 9x)3/2 + C 3. u = x2, du = 2xdx, 1 2 ? sec2 u du = 1 2 tanu+ C = 1 2 tan(x2) + C 4. u = x2, du = 2xdx, 2 ? tanu du = ?2 ln | cosu |+ C = ?2 ln | cos(x2)|+ C 5. u = 2 + cos 3x, du = ?3 sin 3xdx, ? 1 3 ? du u = ?1 3 ln |u|+ C = ?1 3 ln(2 + cos 3x) + C 6. u = 3x 2 , du = 3 2 dx, 2 3 ? du 4 + 4u2 = 1 6 ? du 1 + u2 = 1 6 tan?1 u+ C = 1 6 tan?1(3x/2) + C 7. u = ex, du = exdx, ? sinhu du = coshu+ C = cosh ex + C 8. u = lnx, du = 1 x dx, ? secu tanu du = secu+ C = sec(lnx) + C 9. u = cotx, du = ? csc2 xdx, ? ? eu du = ?eu + C = ?ecot x + C
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