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Unit 6: Интеграл ба өөрчлөлтийн хуримтлал
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The definite integral of a function gives us the area under the curve of that function. Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.
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- Left & right Riemann sumsGet 3 of 4 questions to level up!
- Over- and under-estimation of Riemann sumsGet 3 of 4 questions to level up!
- Midpoint & trapezoidal sumsGet 3 of 4 questions to level up!
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- Summation notationGet 3 of 4 questions to level up!
- Riemann sums in summation notationGet 3 of 4 questions to level up!
- Definite integral as the limit of a Riemann sumGet 3 of 4 questions to level up!
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Суръя
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- Functions defined by definite integrals (accumulation functions)Get 3 of 4 questions to level up!
- 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!
Суръя
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- Finding definite integrals using area formulasGet 3 of 4 questions to level up!
- Finding definite integrals using algebraic propertiesGet 3 of 4 questions to level up!
- Definite integrals over adjacent intervalsGet 3 of 4 questions to level up!
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- Тодоррхой интеграл ба калкулусын үндсэн теоремGet 3 of 4 questions to level up!
- Antiderivatives and indefinite integralsGet 3 of 4 questions to level up!
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Суръя
Дадлага ажил
- 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!
Суръя
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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!
Суръя
Дадлага ажил
- 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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Суръя
Дадлага ажил
- 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 using long divisionGet 3 of 4 questions to level up!
- Integration using completing the squareGet 3 of 4 questions to level up!
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