APEX Calculus - Integration

Overview

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Dive into a comprehensive video series on integration in calculus, covering antiderivatives, definite integrals, Riemann sums, and the Fundamental Theorem of Calculus. Learn through numerous examples and proofs, exploring topics such as initial value problems, geometric applications, and integration techniques like substitution. Master the concepts of partitions, summation notation, and the Mean Value Theorem for integrals. Enhance your understanding of calculus with practical applications, including velocity problems and area between curves.

Syllabus

Integration: Antiderivatives - 01. Intro.
Integration: Antiderivatives - 02. Definition and Indefinite Integrals.
Integration: Antiderivatives - 03. Example.
Integration: Antiderivatives - 04. Example.
Integration: Antiderivatives - 05. Initial Value Problems.
Integration: Antiderivatives - 06. Example.
Integration: Antiderivatives - 07. Example.
Integration: Definite - 01. Intro.
Integration: Definite - 02. Example with Velocity.
Integration: Definite - 03. Definition.
Integration: Definite - 04. Example.
Integration: Definite - 05. Properties.
Integration: Definite - 06. Geometric Examples.
Integration: Definite - 07. Example.
Integration: Riemann - 01. Introduction.
Integration: Riemann - 02. Approximation.
Integration: Riemann - 03. Summation Notation.
Integration: Riemann - 04. Summation Examples.
Integration: Riemann - 05. Summation Properties.
Integration: Riemann - 06. Partitions.
Integration: Riemann - 07. Example.
Integration: Riemann - 08. Definition.
Integration: Riemann - 09. Example.
Integration: Riemann - 10. Example with n Rectangles.
Integration: Riemann - 11. Example With Limit.
Integration: Riemann - 12. Limit of Riemann sum gives definite integral.
Integration: FTC - 01. Intro.
Integration: FTC - 02. Example.
Integration: FTC - 03. FTC Part I.
Integration: FTC - 04. Example.
Integration: FTC - 05. FTC Part II.
Integration: FTC - 06. Proof.
Integration: FTC - 07. Example.
Integration: FTC - 08. Examples.
Integration: FTC - 09. FTC and Chain Rule.
Integration: FTC - 10. Examples.
Integration: FTC - 11. Area Between Curves.
Integration: FTC - 12. Example.
Integration: FTC - 13. Example.
Integration: FTC - 14. MVT for Integrals.
Integration: FTC - 15. Average Value.
Techniques of Integration: Substitution - 01. Intro.
Techniques of Integration: Substitution - 02. Definite integrals.
Techniques of Integration: Substitution - 03. Examples.
Techniques of Integration: Substitution - 04. Example.
Techniques of Integration: Substitution - 05. Examples.
Techniques of Integration: Substitution - 06. Trig Examples.
Techniques of Integration: Substitution - 07. Definite Integral Example.