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Unit: Antiderivatives and the fundamental theorem of calculus

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Antiderivatives and indefinite integrals intro

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

Fundamental theorem of calculus

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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

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Indefinite integrals: reverse power rule

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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

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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

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Finding definite integrals

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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!

Quiz 3

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𝘶-substitution

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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!

Average value of a function

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

Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ

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

Quiz 4

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Optional videos

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Unit test

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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.