Antiderivatives and the Fundamental Theorem: Free Course

About this course

Antiderivatives and accumulation are linked by the fundamental theorem of calculus. This course develops that connection and extends the calculation toolkit through substitution, integration by parts and improper integrals. Study the complete public source playlist from Khan Academy in English, with all 44 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Connect antiderivatives with definite integrals.
• Differentiate accumulation functions using the fundamental theorem.
• Choose substitution, rewriting or integration by parts.
• Evaluate improper integrals through limits and convergence reasoning.

Skills you’ll gain

• Fundamental theorem
• Antiderivatives
• Integration by parts
• Improper integrals

Course Overview

Reverse differentiation begins with the power rule, sums and common trigonometric, exponential and logarithmic functions. The fundamental-theorem recordings connect a variable-limit integral with a derivative and a definite integral with endpoint evaluation. Average-value examples add interpretation. Substitution and algebraic rewriting prepare more complicated integrands; the later examples include integration by parts, partial fractions and limits with infinite bounds. A divergent improper-integral example makes convergence a question that must be answered explicitly. The playlist combines AB material with BC techniques, so it is useful to distinguish the shared foundations from the advanced methods instead of assuming every integral uses the same procedure.

How to study the course

• Videos 1–11: this part of the source list includes “Calculating average value of function over interval” through “Divergent improper integral”. 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 12–22: this part of the source list includes “Fundamental theorem of calculus (Part 1)” through “Reverse power rule”. 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 23–33: this part of the source list includes “Finding derivative with fundamental theorem of calculus: x is on lower bound” through “Definite integral of trig function”. 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 34–44: this part of the source list includes “Integration by parts: ºx____dx” through “Definite integrals: reverse power rule”. 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

Create a short method-selection notebook with one substitution problem, one integration-by-parts problem and one improper integral. Explain the structural clue behind each method. Verify an indefinite answer by differentiation. For the improper example, write the limiting definition and justify convergence or divergence before reporting a value.

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.