Antiderivatives: AP Calculus AB: Free Course

About this course

Antidifferentiation and accumulated change are connected by the fundamental theorem. This AP Calculus AB sequence develops basic antiderivatives, substitution, variable-limit integrals and average value. Study the complete public source playlist from Khan Academy in English, with all 33 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Find basic antiderivatives and indefinite integrals.
• Apply substitution and algebraic rewriting.
• Use both parts of the fundamental theorem.
• Interpret average value and variable-limit integrals.

Skills you’ll gain

• Antiderivatives
• Substitution
• Fundamental theorem
• Average value

Course Overview

Reverse power-rule examples and integrals of familiar trigonometric, exponential and logarithmic functions build the calculation foundation. Sums, multiples and algebraic rewriting extend that toolkit. Substitution identifies a composition that can be simplified with a change of variable. The fundamental-theorem recordings then connect differentiation of an accumulation function with evaluation of a definite integral; examples include a variable lower bound or two variable bounds. Piecewise and absolute-value functions require attention to intervals. Average-value lessons add a contextual interpretation. This AB topic sequence does not include the broader BC integration-by-parts and improper-integral curriculum.

How to study the course

• Videos 1–8: this part of the source list includes “Calculating average value of function over interval” 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 9–16: this part of the source list includes “Intuition for second part of fundamental theorem of calculus” through “Definite integral of absolute value function”. 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 17–24: this part of the source list includes “Reverse power rule” through “Indefinite integrals of sin(x), cos(x), and e_”. 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 25–33: this part of the source list includes “Rewriting before integrating” through “Indefinite integral of 1/x”. 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

Find an antiderivative and verify it by differentiation. Evaluate a definite integral using the corresponding endpoint calculation, then compare it with a graphical interpretation. Build an accumulation function with a variable limit and differentiate it carefully. Explain the role of the constant of integration in the indefinite answer.

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.