Definite Integral Applications: AP Calculus BC: Free Course

About this course

Definite integrals can describe net change, area, volume and curve length. This AP Calculus BC applications course develops those interpretations across rectangular, parametric and polar representations. Study the complete public source playlist from Khan Academy in English, with all 46 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Interpret integrals as net change and motion quantities.
• Set up disk, washer, shell and cross-section volumes.
• Find areas involving rectangular or polar curves.
• Build arc-length integrals for ordinary and parametric curves.

Skills you’ll gain

• Integral applications
• Solids of revolution
• Polar area
• Arc length

Course Overview

Rate and motion examples distinguish accumulated signed change from total distance. Geometric applications build areas between curves and volumes from cross sections, disks, washers and shells. Rotation around shifted horizontal or vertical lines requires a fresh description of radii or shell dimensions. BC extensions introduce arc length, parametric motion and areas bounded by polar curves, including a cardioid. The source retains all parts of multipart demonstrations and its original order. The setup is the main analytical task: choose a variable, interval and geometric quantity that match the representation before choosing an integration technique or calculator command.

How to study the course

• Videos 1–11: this part of the source list includes “Worked example: Area enclosed by cardioid” through “Horizontal area between curves”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 12–23: this part of the source list includes “Parametric curve arc length” through “Worked example: arc length”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 24–34: this part of the source list includes “Shell method for rotating around horizontal line” through “Calculating integral disc around vertical line”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 35–46: this part of the source list includes “Washer method rotating around vertical line (not y-axis), part 2” through “Part 2 of shell method with 2 functions of y”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Draw one planar region and compare two legitimate volume setups where the geometry permits them. Label every radius, height and bound. Add a polar-area or parametric-arc-length example and explain what changes in the formula because of the representation. Check units and compare with an easy special case before accepting the numerical result.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.