This course on Applications of Integration aims to teach students how to calculate areas between curves, volumes by cross-section and cylindrical shells, arc length, and surface area using integration. The course covers various examples and scenarios to help learners understand and apply these concepts effectively. The intended audience for this course is students studying calculus or anyone interested in deepening their understanding of integration applications. The teaching method includes theoretical explanations, step-by-step examples, and problem-solving sessions to enhance comprehension and application of the concepts.
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
