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Written Introduction
Video Introduction
Worked Examples
(5.4)
Indefinite Integrals & Net Change Theorem
Indefinite Integrals (Paul)
Definite Integrals (Paul)

Indefinite Integrals (Incognito)
Definite Integrals (Incognito)
The Indefinite Integral (Khan)
The Power Rule (Khan)
Integral of 1/x (Khan)
Integral of sin(x), cos(x), e^x (Khan)
The Definite Integral (Khan)
Net Change via Integration (Khan)
Indefinite Integral (Khan)
Definite Integral (Khan)

Indefinite Integrals (PatrickJMT)
Definite Integral (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(5.5)
The Substitution Rule
Substitution Rule (Paul)

Substitution Rule (Incognito)
The Substitution Rule (Khan)
u-Sub with Definite Integrals (Khan)

u-Sub Definite Integrals (PatrickJMT)

The Motivation for u-sub (BPRP)
u-Sub Indefinite Integral (Khan)
u-Sub Indefinite Integral (Khan)
u-Sub Indefinite Integral (Khan)

u-Sub Indefinite Integral (PatrickJMT)
u-Sub Indefinite Integral (PatrickJMT)
u-Sub Definite Integral (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(6.1)
Area Between Two Curves
Area Between Curves (Paul)

Area Between Curves (Incognito)
Area Between Two Curves (Khan)
Area Between Two Curves (Khan)

Two Curves w/ x (PatrickJMT)
Two Curves w/ y (PatrickJMT)
Area Between Two Curves (Khan)
Area Between Three Curves (Khan)

Two Curves w/ y (PatrickJMT)
Three Curves (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(6.2)
Volumes by Disks & Washers
Volume w/ Disks & Washers (Paul)

Solids of Revolution (Incognito)
Disk Method Horiz Axis (Khan)
Disk Method Vert Axis (Khan)
Washer Method Horiz Axis (Khan)

Disk & Washer Methods (PatrickJMT)

Disk Method (BPRP)
Disk w/ Horiz Axis (Khan)
Washer w/ Horiz Axis (Khan)
Washer w/ Vert Axis (Khan)

Washer w/ Horiz Axis (PatrickJMT)
Washer w/ Horiz Axis (PatrickJMT)
Washer w/ Vert Axis (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(6.3)
Volumes by Cylindrical Shells
Volume w/ Shells (Paul)

Solids of Revolution (Incognito)
Shell w/ Vert Axis (Khan)
Shell w/ Horiz Axis (Khan)
Two Functions w/ Vert Axis (Khan)
Two Functions w/ Horiz Axis (Khan)

Shell Method (PatrickJMT)
Shell Integral (Khan)
Shell Integral (Khan)
Shell Integral (Khan)

Shell Method (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(6.5)
Average Value of a Function
Ave Value of Function (Paul)

Ave Value of Function (Incognito)
Ave Value of Function (Khan)

Ave Value of Function (PatrickJMT)
Ave Value Example (Khan)
Self-Quiz
Hints
Key
(7.1)
Integration by Parts
Integration by Parts (Paul)

Integration by Parts (Incognito)
Integration by Parts (Khan)

Integration by Parts (BPRP)
Integration by Parts (Khan)
IBP Applied Twice (Khan)
Integration by Parts (Khan)
Loopy IBP Example (Khan)

Definite Integral w/IBP (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Hints
Key
(7.2)
Trigonometric Integrals
Trigonometric Integrals (Paul)

Trigonometric Integrals (Incognito)
Intro to Trig Integrals (BPRP)
Sin & Cos - Odd Pwr (PatrickJMT)
Sin & Cos - Even Pwrs (PatrickJMT)
Sec & Tan - Even Sec (PatrickJMT)
Sec & Tan - Odd Tan (PatrickJMT)

Definite Integral w/Trig (BPRP)

Additional Examples (Dahal)
Self-Quiz
Hints
Key


(7.3)
Trigonometric Substitution
Trig Substitution (Paul)

Trig Substitution (Incognito)
Trig Substitution (Khan)
Indefinite Integral (Khan)
Indefinite Integral - Part 1 (Khan)
Indefinite Integral - Part 2 (Khan)

Indefinite Integral (PatrickJMT)
Definite Integral (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(7.4)
Integration of Rational Functions by Partial Fractions
Partial Fractions (Paul)

Partial Fractions (Incognito)
P.F.D. Linear Factors (Dr. Burger)
P.F.D. Quadratic Factor (Dr. Burger)
P.F.D. Repeated Factor (Dr. Burger)
Linear Factors (Khan)
Repeated Factors (Khan)
Long Division First Step (Khan)

Quadratic Factor (PatrickJMT)
Multiple Examples (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(7.5)
Strategy for Integration
Integration Strategy (PatrickJMT)
Strategy Discussion (PatrickJMT)
Many Examples (BPRP)
(7.8)
Improper Integrals
Improper Integrals (Paul)

Improper Integrals (Incognito)
Improper Integrals (Khan)

Improper Integrals (PatrickJMT)
Divergent Example (Khan)
Both Bounds Infinite (Khan)

Infinite Discontinuity (PatrickJMT)
Subtle Infinite Discont. (PatrickJMT)
Limit w/L'Hopital (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(8.1)
Arc Length
Arc Length (Paul)

Arc Length (Incognito)
Arc Length (Khan)
Arc Length (Khan)
Arc Length (Khan)

Arc Length (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(9.3)
Separable Equations
Separable Equations (Paul)

Separable Equations (Incognito)
Separable Equations (Khan)
Multiple Examples (Khan)

Separable Equation (PatrickJMT)
Separable Equation (PatrickJMT)
With Initial Condition (PatrickJMT)
With Initial Condition (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(11.1)
Sequences
Sequences (Paul)
Sequences (PatrickJMT)

Defining Sequences (Khan)
Convergent Sequence (Khan)

Limit of a Sequence (PatrickJMT)
More Sequence Limits (PatrickJMT)
Recursive Definitions (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key


(11.2)
Infinite Series
Infinite Series Fundamentals (Paul)
Convergence of Infinite Series (Paul)
Geometric & Teloscoping Series (Paul)

Divergence Test (Incognito)
Geometric Series (Incognito)
Teloscoping Series (Incognito)
Sigma Notation (Khan)
Divergence Test (Khan)
Geometric Series (Khan)

Series Introduction (PatrickJMT)

Convergence of Terms/Series (BPRP)
Geometric Series (PatrickJMT)
Telescoping Series I (PatrickJMT)
Telescoping Series II (PatrickJMT)

Geometric Series (BPRP)
Divergence Test I (BPRP)
Divergence Test II (BPRP)

Additional Examples (Dahal)
Self-Quiz
Key
(11.3)
Integral Test
Integral Test (Paul)

Integral Test (Incognito)
Integral Test (Khan)
More Integral Test (Khan)

Integral Test (PatrickJMT)
p-Series (PatrickJMT)

p-Integrals (BPRP)
Integral Test I (PatrickJMT)
Integral Test II (PatrickJMT)
Integral Test III (PatrickJMT)
Integral Test IV (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(11.6)
Ratio and Root Tests
Ratio Test (Paul)
Root Test (Paul)

Ratio Test (Incognito)
Root Test (Incognito)
Ratio Test (Khan)

Ratio Test (PatrickJMT)
Root Test (PatrickJMT)
Ratio Test I (PatrickJMT)
Ratio Test II (PatrickJMT)
Root Test I (PatrickJMT)
Root Test II (PatrickJMT)
Root Test III (PatrickJMT)

Additional Examples (Dahal)
Self-Quiz
Key
(11.8)
Power Series
Power Series (Paul)

Power Series (Incognito)
Power Series (Khan)
Radius of Convergence (Khan)

Radius of Convergence (PatrickJMT)
Interval of Convergence (PatrickJMT)
Interval of Convergence2 (PatrickJMT)

Interval of Convergence (BPRP)
Interval of Convergence2 (BPRP)

Additional Examples (Dahal)
Self-Quiz
Key
(11.10 & 11.11)
Taylor Series & Taylor Polynomials
Taylor Series (Paul)
Taylor Polynomials (Paul)

Taylor Series/Polynomials (Incognito)
Taylor Series a=0 (Khan)
Taylor Series w/nonzero a (Khan)
Visual of Taylor Polynomials (Khan)

Taylor Series (PatrickJMT)
Taylor Series Example (Khan)

Taylor Series Example (PatrickJMT)
Taylor Poly I (PatrickJMT)
Taylor Poly II (PatrickJMT)

Taylor Series I (BPRP)
Taylor Series II (BPRP)

Additional Examples (Dahal)
Self-Quiz
Key