Definite Integral Applications: AP Calculus AB: Free Course

About this course

Integral applications depend on choosing the quantity being accumulated. This source sequence connects net change, motion, areas and volumes using several geometric methods. Study the complete public source playlist from Khan Academy in English, with all 37 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 definite integrals as net change and motion quantities.
• Set up areas between curves.
• Use cross sections, disks, washers and shells for volume.
• Handle rotation about horizontal or vertical shifted axes.

Skills you’ll gain

• Net change
• Area between curves
• Volume integrals
• Shell method

Course Overview

Motion examples distinguish position change from total distance, and rate functions extend the same interpretation to other contexts. Area-between-curves lessons require deciding which boundary is upper or rightmost over the chosen interval. Cross sections, disks, washers and shells provide different descriptions of volume, including rotations about shifted axes. Although the source carries an AP Calculus AB label, it includes shell-method demonstrations; all of those recordings remain available rather than being removed to enforce a narrower syllabus. Multipart explanations are preserved. Choose a slicing direction and label the relevant dimensions before integrating, because the same region can lead to different valid setups.

How to study the course

• Videos 1–9: this part of the source list includes “Calculating integral with shell method” through “Worked examples: interpreting definite integrals in context”. 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 10–18: this part of the source list includes “Analyzing motion problems: total distance traveled” through “Shell method with two functions of x”. 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 19–27: this part of the source list includes “Motion problems with integrals: displacement vs. distance” through “Washer method rotating around vertical line (not y-axis), part 2”. 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 28–37: this part of the source list includes “Disc method rotating around vertical line” 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 a bounded region and set up an area integral. Rotate a suitable region and write a washer or shell integral, labeling the axis and dimensions. Explain the difference between a radius and a height in the chosen method. Add a velocity example and compare displacement with total distance when the velocity changes sign.

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.