10/8/2021

## 10.2 Usubstitution Indefinite Integralsap Calculus

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Substitution is just one of the many techniques available for finding indefinite integrals (that is, antiderivatives). Let's review the method of integration by substitution and get some practice for the AP Calculus BC exam. The Substitution Rule Integration by substitution, also known as u-substitution, after the most common variable for substituting, allows you to reduce a complicated. Indefinite integral problems come in many different types on the AP Calculus Exams. Remember that an indefinite integral is the most general antiderivative of a function. Among the wide range of techniques available, most problems can be handled by one or more of the following methods.

LINK TO SCREENCAST LESSON VIDEOS HERE!!!

The topics below are both AB and BC topics. The topics preceded with an asterisk (*) are BC only topics. All documents are .pdf

Course Info:

1st Day Handout: Parent/Student Letter

1st Day Homework: Academic Integrity, Parent Survey, Student Survey

AP Calculus Syllabus: AB, BC

Open House Info: AB & BC, Bingo, & Schedule

AP Calculus Survival Guide

Appendix: Precalculus stuff to know cold (Notes)

Appendix: Parent Function Catalog (Notes)

Appendix: The Unit Circle (Notes)

Spleen: Prerequisite Algebra Skills (WS/KEY)

Chapter P: Calculus Prerequisites

P.1 What is AP Calculus? (Notes)

P.2 Parent Functions (Notes, WS/KEY)

P.3 Simplifying Expressions (Notes, WS/KEY)

P.4 Equations of Lines (Notes, WS)

P.5 Domain, Range, and Symmetry (Notes, WS)

P.6 Fun with Functions (Notes, WS)

P.7 Trigonometry (Notes, WS)

Chapter 1: Limits

1.1 Limits & Continuity (Notes/E01/E02-06/E07-09/E010-11/E11-12a/E12b-13, WS/KEY)

1.2 Properties of Limits (Notes/E01-02/E03/, WS/KEY)

1.3 Limits at Infinity (Notes/E01-02/E03-04/E04intro/E04-05/E06-07/, WS/KEY)

1.4 Algebraic Limits (Notes/E01-06/E07/E08-12a/E12b-13a/E13b-15d/E15e-h/E15i-16e/E16/, WS/KEY)

1.4 Xtra Practice (WS/KEY)

1.5 Continuity on Intervals & IVT (Notes/E01-03/E03-06b/E6-10/, WS/KEY)

Chapter 2: Differentiation

2.1 Tangent Line & Differentiability (Notes/E01/E01-03/E04-06/E07-09/E10/E11-13/E12-14, WS/KEY)

2.2 Derivatives on the Calculator (Notes/EA/, WS/KEY)

2.3 Basic Differentiation Rules (Notes/E01-06/E07-10/E10-12/E11-12/E13/, WS/KEY)

2.4 Product & Quotient Rules (Notes/E01/E02-03/E04/E05-08/E08-10/E11/, WS/KEY)

2.5 Rates of Change and Particle Motion I (Notes/E01-05/E06/E07-08/E09/, WS/KEY)

2.6 The Chain Rule (Notes/E01a/E01b-f/E01g-04/E05-08/, WS/KEY)

2.7 Implicit Differentiation (Notes/E01-03/E03-06/07a-c/07d-09/E10/, WS/KEY)

2.8 Derivatives of Inverse & Inverse Trig Functions (Notes/E01/E02-03/E4-9/E08-10/E11-13/, WS/KEY)

2.9 Derivatives of Exponential Functions (Notes/E01/E02-05c/E05d-e/E06-07/E08-10/, WS/KEY)

2.10 Derivatives of Log Functions & LOG DIFF (Notes/E01-06/E07-12/, WS/KEY)

### 10.2 U-substitution Indefinite Integralsap Calculus Integrals

Chapter 3: Applications of Differentiation

3.1 Extrema on an interval (Notes/E1-3/E4-6/E7-8/E9/E10-11/, WS/KEY)

3.2 Rolle's Theorem and the MVT (Notes/E1-2/E3-5/E6/E7/, WS/KEY)

3.3 Increasing, Decreasing, and 1st Derivative Test (Notes/E1-2/E3/E4-5/E6-7/E8/, WS/KEY)

3.4 Concavity and the Second Derivative Test (Notes/E1-2/E3-4a/E4b-c/E4d-e/E4f-6c/E6d-7d/E7e-8/, WS/KEY)

3.5 f, f ', and f '(Notes/E1-2b/E1/E2/E3-4/, WS/KEY)

3.5B Summary Sheet (Notes)

3.6 Optimization (Notes/E1/E1-2/E2-6/E6-9/E10-11/E13-14/, WS/KEY)

3.7 Linearization and Differentials (Notes/E1-2/E3-6, WS/KEY)

3.8 Related Rates (Notes/E1-3/E4-5/E6-7/E8-11/, WS/KEY)

Chatper 4: Integration

4.1 Antiderivatives and Indefinite Integration (Notes/E1-3/E4/E5-6d/E6e-f/, WS/KEY)

4.1B Basic Differentiation Practice (WS/KEY)

4.1C Mixed AP MC Review (WS)

### 10.2 U-substitution Indefinite Integralsap Calculus Definition

4.2 Numeric Definite Integrals (Notes/E1/E2a-c/E2d-3/E4-7/E8-9/E10-13/E14/, WS/KEY)

4.3 The FTOC I & II and MVT II (Notes/E1/E1b-4/E5-9a/E8-11/E12-13/E14-17/E18-20/E21/, WS/KEY)

4.4 Integration by u-Substitution (Notes/E1-4/E3-8/E9-13/E13-18b/E18b-24a/E24bce/E24d-25/E24c-e/E25-26, WS/KEY)

Chapter 5: Differential Equations & Modeling

5.1 Separable Differential Equations (Notes/E1-3/E4-8/E9-12/, WS/KEY)

5.2 Slope Fields (Notes/E1-7/E8-17/, WS/KEY)

5.2B Mega Integration Practice (AB methods) (WS)

5.3 *Euler's Method (Notes/E1a/E1b-4/, WS/KEY)

5.4 *Integration by Parts (Notes/E1-8/E8-12/E12-13/, WS/KEY)

5.5 *Partial Fractions & Logistic Growth (Notes/E1-3/E4-8b/, WS/KEY)

Chapter 6: Applications of Integration

6.1 Integral as Net Change (Notes/E1-3/E4-5/E6-7/E9, WS/KEY)

6.2 Area between Curves (Notes/E1-5/E4-7a/E5-7/E8/, WS/KEY)

6.3 Volumes (Notes/E1-4/E4-7c/E7-8/E7d-8a/E8b-9/E10-10c/, WS/KEY)

6.4 *Arc Length (Notes/E1-2/E3-6, WS/KEY)

6.5 L'HÃ´pital's Rule and Indeterminate Forms (Notes/E1-3b/E3c-d/4-5/6-7b/7c-9/, WS/KEY)

6.6 *Improper Integrals (Notes/E1-3/E4-7/E8-11b/E11c-15/E16-19, WS/KEY)

Chatper 7: Vector Calculus

7.1 *Intro to Parametric & Vector Calculus (Notes/E1-3/E4-9, WS/KEY)

7.2 *Parametric & Vector Accumulation (Notes/E1-2, WS/KEY) Worksheet II/KEY

### 10.2 U-substitution Indefinite Integralsap Calculus Calculator

Chapter 8: Polar Calculus

8.1 *Polar Intro & Derivatives (Notes/E1-2a/E2b-3/E4-7a/E7b-10/, WS/KEY)

8.2 *Polar Area (Notes/E1-2/E3-6/E7-8, WS/KEY)

Chapter 9: Sequences & Series

9.1 *Infinite Sequences & Series (Notes/E1-4/E5-8/E9-11/E12-15/E16-20a/E20b-22, WS/KEY)

Summary of Tests for Convergence and Series Flow Chart with practice problems

9.2 *Taylor Polynomials (Notes/E1-3/E4-8/, WS/KEY)

9.3 *Power Series I: Taylor & Maclaurin Series (Notes/E1-2a/E2a-2d/E3-5/E6-9/, WS/KEY)

9.4 *Power Series II: Geometric Series (Notes/E1-7/E7-11/E12/E13/, WS/KEY)

9.5 *Lagrange Error Bound (Notes/E1-4/E5, WS/KEY)

Chapter 10: After the AP Exam

10.1 Trig Substitution Integration (Notes/KEY, WS/KEY)

10.2 Partial Fraction Decomposition (Notes/KEY, WS/KEY)

10.3 Epsilon-Delta Proofs (Notes/KEY, WS/KEY)

10.4 Newton's Method (Notes/KEY, WS/KEY)

### 10.2 U-substitution Indefinite Integralsap Calculus Solver

10.5 Surface Area (Notes/KEY, WS/KEY)

10.6 Hyperbolic Trig Functions (Notes/KEY, WS/KEY)

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