Math 201-NYB-05
Integral Calculus

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Tests
Test #1 -
Test #2 -
Test #3 -



MyYouTube

1.
 1:22:23
Review of Differentiation - 1 - pdf
Review of Differentiation - 2 - pdf
Review of Differentiation - 3 - pdf
Review of Differentiation - 4 - pdf
Review of Differentiation - 5 - pdf
Review of Differentials - pdf
Review of Limits at Infinity - pdf
Review of L'H˘pital's Rule - 1 - pdf
Review of L'H˘pital's Rule - 2 - pdf
Review of L'H˘pital's Rule - 3 - pdf
2.
  1:46:56
Antiderivatives - 1 - pdf
Antiderivatives - 2 - pdf
Simple Differential Equation - 1 - pdf
Simple Differential Equation - 2 - pdf
Indefinite Integrals - 1 - pdf
Indefinite Integrals - 2 - pdf
Indefinite Integrals - 3 - pdf
Indefinite Integrals - 4 - pdf
Indefinite Integrals - 5 - pdf
3.
  2:11:04
Sigma Notation - 1 - pdf
Sigma Notation - 2 - pdf
Riemann Sum - 1 - pdf
Riemann Sum - 2 - pdf
Riemann Sum - 3 - pdf
The Definite Integral - pdf
4.
  1:30:27
The Fundamental Theorem of Calculus - Introduction - pdf
The Fundamental Theorem of Calculus - Notation - pdf
The Fundamental Theorem of Calculus - Proof - pdf
The Fundamental Theorem of Calculus - Example 1 - pdf
The Fundamental Theorem of Calculus - Example 2 - pdf
  (Additional)
  
(Example 2 is a slightly more elaborate example than 1.)
The Fundamental Theorem of Calculus - Example 3 -
pdf
Average Value of a Function -
pdf
Mean Value Theorem of Integration -
pdf  (Optional)
MVT of Integration - Comment -
pdf  (Optional)
Limits & the Fundamental Theorem of Calculus -
pdf  (Optional)
5.
  1:44:57
U-Substitution - 1 -
pdf
U-Substitution - 2 -
pdf
U-Substitution - 3 -
pdf
U-Substitution - 4 -
pdf
U-Substitution - 5 -
pdf
U-Substitution - 6 -
pdf
U-Substitution - 7 -
pdf
U-Substitution - 8 -
pdf
U-Substitution & Trig. Functions - 1 -
pdf
U-Substitution & Trig. Functions - 2 -
pdf
6.
  1:09:27
Integration by Parts - 1 -
pdf
Integration by Parts - 2 -
pdf
Integration by Parts - 3 -
pdf
Integration by Parts - 4 -
pdf
Integration by Parts - 5 -
pdf
Integration by Parts - 6 -
pdf
7.
  1:09:49
Area Between Curves - 1
(Solution 1) - pdf
Area Between Curves - 1
(Solution 2) - pdf
Area Between Curves - 2
(Solution 1) - pdf
Area Between Curves - 2
(Solution 2) - pdf
Area Between Curves - 3 -
pdf
Area Between Curves - 4 -
pdf  (Optional)
8.
  1:16:27
Solids of Revolution - Disk -
pdf
Solids of Revolution - Washer -
pdf
Solids of Revolution - Shell -
pdf
Solids of Revolution - Example 1 -
pdf
Solids of Revolution - Example 2 -
pdf
Solids of Revolution - Example 3 -
pdf
Solids of Revolution - Example 4 -
pdf
9.
  34:17
Solids & Cross Sections - 1 -
pdf
Solids & Cross Sections - 2 -
pdf
Solids & Cross Sections - 3 -
pdf
10.
  38:13
Separable Differential Equations - 1 -
pdf
The Slope of Orthogonal Lines -
pdf
Orthogonal Families of Curves - 1 -
pdf
Orthogonal Families of Curves - 2 -
pdf
11.
  1:28:49
Trigonometric Integrals - 1 -
pdf
Trigonometric Integrals - 2 -
pdf
Trigonometric Integrals - 3 -
pdf
Trigonometric Integrals - 4 -
pdf
Trigonometric Integrals - 5 -
pdf
Trigonometric Integrals - 6 -
pdf
Trigonometric Integrals - 7 -
pdf
12.
  8:53
Completing Squares -
pdf
13.
  1:33:48
Trigonometric Substitutions - Introduction
- pdf
Trigonometric Substitutions - 1
- pdf
Trigonometric Substitutions - 2 -
pdf
Trigonometric Substitutions - 3
- pdf
Trigonometric Substitutions - 4 -
pdf
Trigonometric Substitutions - 5 -
pdf
Trigonometric Substitutions - 6 -
pdf
Trigonometric Substitutions - 7 -
pdf
14.
  2:06:13
Partial Fractions: Introduction - 1 -
pdf
Partial Fractions: Introduction - 2 -
pdf
Partial Fractions: Example 1 -
pdf
Partial Fractions: Example 2 -
pdf
Partial Fractions: Example 3 -
pdf
Partial Fractions: Special Integral - 1 -
pdf
Partial Fractions: Irreducibility & Discriminant -
pdf
Partial Fractions: Example 4 -
pdf
Partial Fractions: Example 5 -
pdf
Partial Fractions: Special Integral - 2 -
pdf
Partial Fractions: Example 6 -
pdf
15.
30:44
Rationalizing Substitutions - 1 -
pdf
Rationalizing Substitutions - 2 -
pdf
Rationalizing Substitutions - 3 -
pdf
16.
  27:23
Arc Length - 1 -
pdf  (Formula - Intuitive Derivation)
Arc Length - 2 -
pdf  (Formula - Rigorous Derivation - Optional)
Arc Length - 3 -
pdf
Arc Length - 4 -
pdf
17.
  0:00
Surface Area - Introduction -
pdf  (Optional)
Surface Area - Example -
pdf  (Optional)
18.
  1:35:39
Improper Integrals - Introduction -
pdf
Improper Integrals of Type 1 - Example 1 -
pdf
Improper Integrals of Type 1 - Example 2 -
pdf
Improper Integrals of Type 1 - Example 3 -
pdf
Improper Integrals of Type 1 - Example 4 -
pdf
Improper Integrals of Type 2 - Example 1 -
pdf
Improper Integrals of Type 2 - Example 2 -
pdf
Improper Integrals of Type 2 - Example 3 -
pdf

The Comparison Theorem - Introduction -
pdf  (Optional)
The Comparison Theorem - Example 1 -
pdf  (Optional)
The Comparison Theorem - Example 2 -
pdf  (Optional)
The Comparison Theorem - Example 3 -
pdf  (Optional)
The Comparison Theorem - Example 4 -
pdf (Optional)
19.
  2:35:06
Sequences - Introduction -
pdf
Sequences - Convergence -
pdf
Sequences & L'H˘pital's Rule -
pdf
Geometric Sequences & Convergence - Intuition -
pdf
Geometric Sequences - Examples -
pdf
Geometric Sequences & Convergence - Proof -
pdf  (Optional)
The Factorial - Introduction -
pdf
The Factorial - Magnitude -
pdf  (Optional)
Hierarchy of Functions -
pdf
The Squeeze Theorem - 1 -
pdf
The Squeeze Theorem - 2 -
pdf
Bounded Sequences -
pdf
Monotonic Sequences -
pdf
Monotone Convergence Theorem - Intuition -
pdf
Monotone Convergence Theorem - Example -
pdf
The Harmonic Series -
pdf
20.
  1:57:35
Introduction to Series - 1 -
pdf
Introduction to Series - 2 -
pdf
Properties of Convergent Series -
pdf
Geometric Series - Formula -
pdf
Geometric Series - Examples -
pdf
Finite Geometric Sums -
pdf
Geometric Series & Decimal Expansion -
pdf
Telescoping Series -
pdf
Divergence Theorem - Introduction -
pdf
Divergence Theorem - Proof -
pdf
Divergence Theorem - Examples -
pdf
21.
  3:04:27
Convergence & Ignoring Terms -
pdf
The Integral Test - Proof -
pdf
The Integral Test - Example 1 -
pdf
The Integral Test - Example 2 -
pdf
P-Series - Proof -
pdf
P-Series - Examples -
pdf
Series of Positive Terms - Intuition -
pdf
The Comparison Test - Intuition -
pdf
The Comparison Test - Example 1 -
pdf
The Comparison Test - Example 2 -
pdf
The Comparison Test - Example 3 -
pdf
The Limit Comparison Test - Intuition -
pdf
The Limit Comparison Test - Proof -
pdf  (Optional)
The Limit Comparison Test - Example 1 -
pdf
The Limit Comparison Test - Example 2 -
pdf
The Limit Comparison Test - Example 3 -
pdf
Alternating Series - Introduction -
pdf
Alternating Series Test - Introduction -
pdf
Alternating Series Test - Proof -
pdf  (Optional)
Alternating Series Test - Example 1 -
pdf
Alternating Series Test - Example 2 -
pdf
Alternating Series Test - Example 3 -
pdf
Alternating Series & Error Estimate - Example -
pdf
Alternating Series & Error Estimate - Proof -
pdf  (Optional)
22.
  1:17:19
Absolute Convergence - Introduction -
pdf
Absolute Convergence Test - Proof -
pdf
Absolute vs Conditional Convergence - Introduction -
pdf
Absolute vs Conditional Convergence - Example 1 -
pdf
Absolute vs Conditional Convergence - Example 2 -
pdf
The Ratio Test - Introduction -
pdf
The Ratio Test - Proof of Part (a) -
pdf  (Optional)
The Ratio Test - Proof of Part (b) -
pdf  (Optional)
The Ratio Test - Proof of Part (c) -
pdf  (Optional)
The Ratio Test - Example 1 -
pdf
The Ratio Test - Example 2 -
pdf
The Ratio Test - Example 3 -
pdf
The Root Test - Introduction -
pdf
The Root Test - Proof of Part (a) -
pdf  (Optional)
The Root Test - Proof of Part (b) -
pdf  (Optional)
The Root Test - Proof of Part (c) -
pdf  (Optional)
The Root Test - Example 1 -
pdf
The Root Test - Example 2 -
pdf
The Root Test - Example 3 -
pdf

 
(This is a pretty neat result!)
Rearrangement - Introduction -
pdf  (Optional)
Riemann's Rearrangement Theorem - Introduction -
pdf  (Optional)
Riemann's Rearrangement Theorem - Example -
pdf  (Optional)
23.
  1:53:49
Power Series: Introduction - 1 -
pdf
Power Series: Introduction - 2 -
pdf
Power Series: Introduction - 3 -
pdf
Interval of Convergence - 1 -
pdf
Interval of Convergence - 2 -
pdf
Interval of Convergence - 3 -
pdf
Differentiation & Integration - Introduction -
pdf
Differentiation & Integration - Part (a) -
pdf
Differentiation & Integration - Part (b) -
pdf
Differentiation & Integration - Part (c) -
pdf
24.
  49:29
Maclaurin & Taylor Series - Introduction -
pdf
Maclaurin Series - Example 1 -
pdf
Maclaurin Series - Example 2 -
pdf
Maclaurin Series - Example 3 -
pdf
Maclaurin Series & Limits - 1 -
pdf (Optional)
Maclaurin Series & Limits - 2 -
pdf (Optional)
Maclaurin Series & Higher Derivatives -
pdf (Optional)
25.
  24:34
Taylor Series - Example 1 -
pdf
Taylor Series - Example 2 -
pdf
Taylor Series - Example 3 -
pdf  (Optional)
Taylor's Theorem - Introduction -
pdf  (Optional)
Taylor's Theorem - e^x - pdf  (Optional)

  Documents
Summary of Differentiation Rules
Trig. Functions & Identities
11. Trigonometric Integrals - Help File

14. The Method of Partial Fractions
20-22. Series - Summary of Tests

Problem Sheets

1-
Review
2- Antiderivatives
3- Riemann Sums & the Definite Integral
4- The Fundamental Theorem of Calculus
5- U-Substitutions
6- Integration by Parts
7- Area Between Curves
8- Solids of Revolution

9- Solids & Cross Sections
10- Differential Equations
11- Trigonometric Integrals 
12- Completing Squares
13- Trigonometric Substitutions
14- Partial Fractions
15- Rationalizing Substitutions 
16- Arc Length
17- Surface Area (
Optional)
18- Improper Integrals
19- Sequences
20- Series #1
21- Series #2
22- Series #3
23- Power Series
24- Maclaurin Series
25- Taylor Series