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# Unit 9: Antiderivatives and the fundamental theorem of calculus

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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.### Learn

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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!

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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!

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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!

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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!

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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!

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

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

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