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1
❖ The Definite Integral - Understanding the Definition ❖
2
Approximating a Definite Integral Using Rectangles
3
❖ Calculating a Definite Integral Using Riemann Sums - Part 1 ❖
4
Calculating a Definite Integral Using Riemann Sums - Part 2
5
❖ Basic Integration Problems
6
❖ Integration by Parts Made Easy! ❖
7
Integration by Parts - Definite Integral
8
Integration By Parts - Using IBP's Twice
9
Integration by Parts - A Loopy Example!
10
Deriving the Integration by Parts Formula - Easy!
11
❖ Integration using U-Substitution ❖
12
Integration by U-Substitution, Definite Integral
13
U-substitution - Indefinite Integral, Another 2 examples
14
U-Substitution - More Complicated Examples
15
Trigonometric Substitution - Example 1
16
Trigonometric Substitution Example 1 Part 1
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Trigonometric Substitution Example 1 Part 2
18
Trigonometric Substitution - Example 2
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Trigonometric Substitution - Example 3 / Part 1
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Trigonometric Substitution - Example 3 / Part 2
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Trigonometric Substitution, Ex 4 - Rational Powers
22
Trigonometric Substitutions - More Examples
23
Trigonometric Substitution and a Definite Integral
24
Trigonometric Substitution + U-Sub, Definite Integral
25
Integrating Exponential Functions - Examples 1 and 2
26
Integrating Exponential Functions - Examples 3 and 4
27
Integration Using Inverse Trigonometric Functions - Ex 1
28
Integration Using Inverse Trigonometric Functions - Ex 2
29
Trigonometric Integrals - Part 1 of 6
30
Trigonometric Integrals - Part 2 of 6
31
Trigonometric Integrals - Part 3 of 6
32
Trigonometric Integrals - Part 4 of 6
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Trigonometric Integrals - Part 5 of 6
34
Trigonometric Integrals - Part 6 of 6
35
Partial Fraction Decompositions and Long Division
36
Integration Using Partial Fractions / Rationalizing Sub
37
Integration Using method of Partial Fractions
38
A Complete Partial Fractions Problem
39
Long Partial Fractions Problem - Repeated Irreducible Quadratic Factors, Part 1
40
Long Partial Fractions Problem - Repeated Irreducible Quadratic Factors, Part 2
41
❖ Improper Integral - Basic Idea and Example ❖
42
Improper Integral with Infinite Discontinuity at Endpoint
43
Improper Integral - Infinity in Upper and Lower Limits
44
Improper Integral w/ Infinite Discontinuity in the Middle
45
Improper Integral - More Complicated Example
46
Hyperbolic Functions - Integration
47
Arc Length
48
Finding Surface Area - Part 1
49
Finding Surface Area - Part 2
50
Parametric Curves - Calculating Area
51
Arc Length Using Parametric Curves
52
Arc Length Using Parametric Curves - Example 2
53
Finding Areas in Polar Coordinates
54
Finding Areas Between Curves
55
Area Between Curves - Integrating with Respect to y
56
Area Between Curves - Integrating with Respect to y - Part 2
57
Longer Version - Volumes using Disks/Washers
58
Volumes of Revolution - Disk/Washers Example 1
59
Volumes of Revolution - Disk/Washers Example 2
60
Volumes of Revolution - Disk/Washers Example 3
61
Volumes of Revolution about Vertical Lines Using Washers
62
Longer Version - Volumes using Cylindrical Shells
63
Volumes of Revolution - Cylindrical Shells
64
The Trapezoid Rule for Approximating Integrals
65
Simpsons Rule - Approximate Integration
66
Simpson's Rule - Error Bound
Description:
Dive into a comprehensive video playlist covering integrals and antiderivatives, starting with various integration methods and progressing to their applications in calculating areas, volumes, and arc lengths. Master topics such as basic definite integrals, integration by parts, trigonometric substitution, partial fractions, improper integrals, and more. Learn to apply these techniques to solve problems involving areas between curves, volumes of revolution, and surface areas. Explore advanced concepts like parametric curves, polar coordinates, and approximation methods including the Trapezoid Rule and Simpson's Rule. Perfect for students and enthusiasts looking to deepen their understanding of calculus and its practical applications.

Integrals - Antiderivatives

patrickJMT
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#Mathematics #Calculus #Integral Calculus #Exponential Functions #Definite Integrals #Improper Integrals #Partial Fractions #Integration by Parts #Trigonometry #Inverse Trigonometric Functions #Trigonometric Integrals #Trigonometric Substitution
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❖ The Definite Integral - Understanding the Definition ❖