Applications of Integration: Free Course

About this course

Integration becomes useful when an accumulated quantity is defined carefully. This course applies definite integrals to average values, motion, net change, areas and the volumes of solids. Study the complete public source playlist from Khan Academy in English, with all 37 recordings available in the on-site classroom. Lessons retain their original titles and source order, including worked examples, introductions and repeated entries.

Course at a glance

What you’ll learn

• Interpret net change and average value using definite integrals.
• Distinguish displacement from total distance traveled.
• Set up areas between curves with appropriate boundaries.
• Build cross-section, disk and washer volume integrals.

Skills you’ll gain

• Integral applications
• Net change
• Area between curves
• Volumes of solids

Course Overview

The first group of lessons connects an integral with the average value of a function and the mean value theorem for integrals. Motion examples distinguish signed displacement from total distance traveled, making the role of positive and negative velocity explicit. Rate-function examples extend that reasoning to other accumulated quantities and emphasize interpretation in context. The geometry section develops area between curves, including boundaries best described horizontally, before moving to volumes with specified cross sections. Disk and washer methods then describe solids of revolution about horizontal and vertical lines, including axes other than the coordinate axes. The main skill is setting up the integral: choose the variable, limits, slice dimensions and sign convention before calculating. A correct antiderivative cannot repair a model whose radius, thickness or interval was chosen incorrectly.

How to study the course

• Videos 1–9: this part of the source list includes “Average value over a closed interval” through “Area under rate function gives the net change”. 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 “Interpreting definite integral as net change” through “Area between curves with multiple boundaries”. 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 “Area between a curve and and the _-axis” through “Generalizing disc method around x-axis”. 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 around y-axis” through “Washer method rotating around vertical line (not y-axis), part 2”. 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

Prepare a worked example in three parts: interpret a velocity integral, find an area between two simple curves and set up a rotated-solid volume. Draw the region and label the bounds before integrating. For the volume, identify outer and inner radii when required. Explain units and signs in each answer and use an easy geometric case to check whether the setup makes sense.

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.