Integration and Accumulation: AP Calculus BC: Free Course

About this course

Accumulation connects sums, definite integrals and antiderivatives. This AP Calculus BC topic sequence builds that connection before extending the calculation toolkit to more demanding integrals. Study the complete public source playlist from Khan Academy in English, with all 70 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

• Express accumulation using sums and definite integrals.
• Apply both parts of the fundamental theorem of calculus.
• Use substitution and algebraic rewriting in integration.
• Recognize when parts, partial fractions or improper-integral limits are needed.

Skills you’ll gain

• Riemann sums
• Fundamental theorem
• Integration methods
• Improper integrals

Course Overview

Riemann, midpoint and trapezoidal sums begin with approximation and lead to the definite integral as a limit. Summation notation helps express the same idea symbolically. The fundamental theorem then links accumulation functions with derivatives and antiderivatives. Properties involving interval direction, adjacent intervals, sums and scaling support interpretation before technique. Basic antiderivatives and substitution are developed through algebraic, trigonometric, logarithmic and exponential examples. The later BC material includes integration by parts, partial fractions and improper integrals, including a divergent example. Proof and intuition recordings return to the fundamental theorem at the end. Treat the course as the integration-and-accumulation portion of the curriculum: its value is in choosing and explaining an appropriate method, not collecting unrelated integration formulas.

How to study the course

• Videos 1–17: this part of the source list includes “Introduction to integral calculus” through “Fundamental theorem of calculus (Part 1)”. 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 18–35: this part of the source list includes “Functions defined by definite integrals (accumulation functions)” through “Fundamental theorem of calculus (Part 2)”. 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 36–52: this part of the source list includes “Antiderivatives and indefinite integrals” through “_-substitution: defining _”. 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 53–70: this part of the source list includes “_-substitution: defining _ (more examples)” through “Intuition for second part of fundamental theorem of calculus”. 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

Estimate an integral from a small table, then compare it with an exact calculation for a chosen function. Build an accumulation function and find its derivative. Prepare separate examples for substitution and integration by parts, explaining the choice of method. For an improper integral, state the required limit and decide whether it converges instead of treating infinity as an ordinary endpoint.

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.