Explore advanced applications of integration in calculus through a comprehensive series of video lectures. Learn to calculate areas between curves, compute volumes using cross-sections and cylindrical shells, determine arc lengths, and find surface areas of various shapes. Master techniques for solving complex problems involving multiple intersections, different coordinate systems, and unique geometric configurations. Gain practical skills in applying integration to real-world scenarios, including the famous Gabriel's Horn problem. Enhance your understanding of calculus concepts through detailed examples and step-by-step problem-solving demonstrations.
APEX Calculus - Applications of Integration
Overview
Syllabus
Applications of Integration: Area between curves - 01. Introduction.
Applications of Integration: Area between curves - 02. Example 1.
Applications of Integration: Area between curves - 03. Example 2, multiple intersections.
Applications of Integration: Area between curves - 04. Example 3, with respect to y.
Applications of Integration: Area between curves - 05. Example 4; a triangle.
Applications of Integration: Volumes by cross-section - 01. Introduction.
Applications of Integration: Volumes by cross-section - 02. Example 1, with square cross-sections.
Applications of Integration: Volumes by cross-section - 03. Example 2, with disks.
Applications of Integration: Volumes by cross-section - 04. Example 3, about y axis.
Applications of Integration: Volumes by cross-section - 05. Example 4, washers (part 1 - setup).
Applications of Integration: Volumes by cross-section - 06. Example 4, washers (part 2 - evaluation).
Applications of Integration: Volume by cross-section - 07. Example 5.
Applications of Integration: Volume by cylindrical shell - 01. Introduction.
Applications of Integration: Volume by cylindrical shell - 02. Example 1.
Applications of Integration: Volume by cylindrical shell - 03. Example 2.
Applications of Integration: Volume by cylindrical shell - 04. Example 3.
Applications of Integration: Volume by cylindrical shell - 05. Example 4.
Applications of Integration: Arc Length - 01. Introduction.
Applications of Integration: Arc Length - 02. Example 1.
Applications of Integration: Arc Length - 03. Example 2.
Applications of Integration: Surface Area - 01. Introduction.
Applications of Integration: Surface Area - 02. Example 1, Part 1.
Applications of Integration: Surface Area - 03. Example 1, Part 2.
Applications of Integration: Surface Area - 04. Example 2, Part (a).
Applications of Integration: Surface Area - 05. Example 2, Part (b).
Applications of Integration: Surface Area - 06. Example 3 - Gabriel's Horn.
Taught by
Sean Fitzpatrick
