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.
Overview
Syllabus
❖ The Definite Integral - Understanding the Definition ❖.
Approximating a Definite Integral Using Rectangles.
❖ Calculating a Definite Integral Using Riemann Sums - Part 1 ❖.
Calculating a Definite Integral Using Riemann Sums - Part 2.
❖ Basic Integration Problems.
❖ Integration by Parts Made Easy! ❖.
Integration by Parts - Definite Integral.
Integration By Parts - Using IBP's Twice.
Integration by Parts - A Loopy Example!.
Deriving the Integration by Parts Formula - Easy!.
❖ Integration using U-Substitution ❖.
Integration by U-Substitution, Definite Integral.
U-substitution - Indefinite Integral, Another 2 examples.
U-Substitution - More Complicated Examples.
Trigonometric Substitution - Example 1.
Trigonometric Substitution Example 1 Part 1.
Trigonometric Substitution Example 1 Part 2.
Trigonometric Substitution - Example 2.
Trigonometric Substitution - Example 3 / Part 1.
Trigonometric Substitution - Example 3 / Part 2.
Trigonometric Substitution, Ex 4 - Rational Powers.
Trigonometric Substitutions - More Examples.
Trigonometric Substitution and a Definite Integral.
Trigonometric Substitution + U-Sub, Definite Integral.
Integrating Exponential Functions - Examples 1 and 2.
Integrating Exponential Functions - Examples 3 and 4.
Integration Using Inverse Trigonometric Functions - Ex 1.
Integration Using Inverse Trigonometric Functions - Ex 2.
Trigonometric Integrals - Part 1 of 6.
Trigonometric Integrals - Part 2 of 6.
Trigonometric Integrals - Part 3 of 6.
Trigonometric Integrals - Part 4 of 6.
Trigonometric Integrals - Part 5 of 6.
Trigonometric Integrals - Part 6 of 6.
Partial Fraction Decompositions and Long Division.
Integration Using Partial Fractions / Rationalizing Sub.
Integration Using method of Partial Fractions.
A Complete Partial Fractions Problem.
Long Partial Fractions Problem - Repeated Irreducible Quadratic Factors, Part 1.
Long Partial Fractions Problem - Repeated Irreducible Quadratic Factors, Part 2.
❖ Improper Integral - Basic Idea and Example ❖.
Improper Integral with Infinite Discontinuity at Endpoint.
Improper Integral - Infinity in Upper and Lower Limits.
Improper Integral w/ Infinite Discontinuity in the Middle.
Improper Integral - More Complicated Example.
Hyperbolic Functions - Integration.
Arc Length.
Finding Surface Area - Part 1.
Finding Surface Area - Part 2.
Parametric Curves - Calculating Area.
Arc Length Using Parametric Curves.
Arc Length Using Parametric Curves - Example 2.
Finding Areas in Polar Coordinates.
Finding Areas Between Curves.
Area Between Curves - Integrating with Respect to y.
Area Between Curves - Integrating with Respect to y - Part 2.
Longer Version - Volumes using Disks/Washers.
Volumes of Revolution - Disk/Washers Example 1.
Volumes of Revolution - Disk/Washers Example 2.
Volumes of Revolution - Disk/Washers Example 3.
Volumes of Revolution about Vertical Lines Using Washers.
Longer Version - Volumes using Cylindrical Shells.
Volumes of Revolution - Cylindrical Shells.
The Trapezoid Rule for Approximating Integrals.
Simpsons Rule - Approximate Integration.
Simpson's Rule - Error Bound.
Taught by
patrickJMT
