If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit: Antiderivatives and the fundamental theorem of calculus

0

Possible mastery points

Antiderivatives and indefinite integrals intro

Learn

Practice

Antiderivatives and indefinite integralsGet 3 of 4 questions to level up!

Fundamental theorem of calculus

Learn

Practice

Finding derivative with fundamental theorem of calculusGet 3 of 4 questions to level up!
Finding derivative with fundamental theorem of calculus: chain ruleGet 3 of 4 questions to level up!
The fundamental theorem of calculus and definite integralsGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 320 Mastery points

Indefinite integrals: reverse power rule

Learn

Practice

Reverse power ruleGet 3 of 4 questions to level up!
Reverse power rule: negative and fractional powersGet 3 of 4 questions to level up!
Reverse power rule: sums & multiplesGet 3 of 4 questions to level up!
Reverse power rule: rewriting before integratingGet 3 of 4 questions to level up!

Indefinite integrals of sin(x), cos(x), eˣ, and 1/x

Learn

Practice

Indefinite integrals: eˣ & 1/xGet 3 of 4 questions to level up!
Indefinite integrals: sin & cosGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 480 Mastery points

Finding definite integrals

Learn

Practice

Definite integrals: reverse power ruleGet 3 of 4 questions to level up!
Definite integrals: common functionsGet 3 of 4 questions to level up!
Definite integrals of piecewise functionsGet 3 of 4 questions to level up!

Improper integrals

Learn

Practice

Improper integralsGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 320 Mastery points

𝘶-substitution

Learn

Practice

𝘶-substitution: defining 𝘶Get 3 of 4 questions to level up!
𝘶-substitution: indefinite integralsGet 3 of 4 questions to level up!
𝘶-substitution: definite integralsGet 3 of 4 questions to level up!

Integration by parts

Learn

Practice

Integration by partsGet 3 of 4 questions to level up!
Integration by parts: definite integralsGet 3 of 4 questions to level up!

Partial fraction expansion

Learn

Practice

Integration with partial fractionsGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 480 Mastery points

Average value of a function

Learn

Practice

Average value of a functionGet 3 of 4 questions to level up!

Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ

Learn

Practice

Interpreting the behavior of accumulation functionsGet 3 of 4 questions to level up!

Optional videos

Learn

Quiz 5

Level up on the above skills and collect up to 160 Mastery points

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 2200 Mastery points!

About this unit

The antiderivative of a function ƒ is a function whose derivative is ƒ. To find antiderivatives of functions we apply the derivative rules in reverse. The fundamental theorem of calculus connects differential and integral calculus by showing that the definite integral of a function can be found using its antiderivative.