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ap calculus ab - integration & ftc review

originally streamed in 2019 with Jamil SiddiquiTeacher
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Review integration techniques and the Fundamental Theorem of Calculus for AP Calculus AB. This session walks through u-substitution, integral properties, and a complete FTC free-response question with detailed explanations to help you prepare for the ...more

covered in this stream

units
Unit 6 – Integration and Accumulation of ChangeUnit 5 – Analytical Applications of DifferentiationUnit 4 – Contextual Applications of DifferentiationUnit 3 – Composite, Implicit, and Inverse Functions
topics
6.9 Integrating Using 1 Substitution6.6 Applying Properties of 3 Definite Integrals6.4 The Fundamental Theorem of Calculus and Accumulation Functions6.5 Interpreting the Behavior of Accumulation Functions Involving Area6.7 The Fundamental Theorem of Calculus and Definite Integrals5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points5.4 Using the First Derivative Test to Determine Relative (Local) Extrema5.5 Using the Candidates Test to Determine Absolute (Global) Extrema5.6 Determining Concavity5.9 Connecting a Function, Its First Derivative, and its Second Derivative 4.6 Approximating Values of a Function Using Local Linearity and Linearization3.1 The Chain Rule

timestamps

  • 0:00

    Integration by Substitution

  • 0:37

    Substitution Example Setup

  • 1:09

    Bounds and DU Calculation

  • 1:40

    U-World Transition

  • 2:10

    Handling X and DX

  • 3:14

    Isolating X DX

  • 3:45

    Substituting Bounds

  • 4:46

    Lower Bound Calculation

  • 5:19

    Selecting Answer D

  • 5:49

    Properties of Integrals

  • 6:50

    Combining Integrals

  • 7:53

    G Minus F Integral

  • 8:57

    Reversing Integrand

  • 10:00

    Breaking Up Integrals

  • 11:03

    Final Integral Value

  • 13:42

    Integral Properties Example

  • 19:08

    Session Outline

  • 19:39

    FTC Super FRQ

  • 20:41

    Graph Geometry

  • 21:43

    FTC Derivative

  • 23:16

    Part A Calculations

  • 26:53

    F Prime at 14

  • 28:28

    Part B Critical Points

  • 31:38

    Part C Inflection Points

  • 34:46

    Increasing and Concave Down

  • 37:59

    Absolute Maximum

  • 41:05

    Labeling Areas

  • 44:17

    Computing F Values

  • 48:57

    H Prime Calculation

  • 50:30

    Tangent Line to H

  • 54:42

    Approximation Analysis

  • 56:47

    H Double Prime

  • 59:25

    FTC Conclusion

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Resources

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history

šŸŒŽ ap world historyšŸ‡ŗšŸ‡ø ap us historyšŸ‡ŖšŸ‡ŗ ap european history

social science

āœŠšŸæ ap african american studiesšŸ—³ļø ap comparative government🚜 ap human geographyšŸ’¶ ap macroeconomicsšŸ¤‘ ap microeconomics🧠 ap psychologyšŸ‘©šŸ¾ā€āš–ļø ap us government

english & capstone

āœšŸ½ ap english languagešŸ“š ap english literaturešŸ” ap researchšŸ’¬ ap seminar

arts

šŸŽØ ap art & designšŸ–¼ļø ap art historyšŸŽµ ap music theory

science

🧬 ap biology🧪 ap chemistryā™»ļø ap environmental sciencešŸŽ” ap physics 1🧲 ap physics 2šŸ’” ap physics c: e&māš™ļø ap physics c: mechanics

math & computer science

🧮 ap calculus abā™¾ļø ap calculus bcšŸ“ ap precalculusšŸ“Š ap statisticsšŸ’» ap computer science aāŒØļø ap computer science p

world languages

šŸ‡ØšŸ‡³ ap chinesešŸ‡«šŸ‡· ap frenchšŸ‡©šŸ‡Ŗ ap germanšŸ‡®šŸ‡¹ ap italianšŸ‡ÆšŸ‡µ ap japanesešŸ›ļø ap latinšŸ‡ŖšŸ‡ø ap spanish languagešŸ’ƒšŸ½ ap spanish literature

go beyond AP

high school exams

āœļø PSATšŸŽ“ Digital SATšŸŽ’ ACT

honors classes

šŸ¬ honors algebra IIšŸ«€ honors anatomyšŸ‡ honors biologyšŸ‘©šŸ½ā€šŸ”¬ honors chemistryšŸ’² honors economicsšŸ“ honors geometryāš¾ļø honors physicsšŸ“ honors pre-calculusšŸ“Š honors statisticsšŸ—³ļø honors us governmentšŸ‡ŗšŸ‡ø honors us historyšŸŒŽ honors world history

college classes

šŸ‘©šŸ½ā€šŸŽ¤ artsšŸ‘” businessšŸŽ¤ communicationsšŸ—ļø engineeringšŸ““ humanitiesāž— mathšŸ§‘šŸ½ā€šŸ”¬ sciencešŸ’¶ social science

hs classes

šŸ›ļø alabama historyā›°ļø appalachian studies🌓 california historyšŸŒ earth science🌐 ethnic studies🐊 florida historyšŸ‘ georgia historyšŸŒŽ global studies🌺 hawaiian studiesšŸ“° journalism🪶 native american studies🌵 new mexico history🤠 oklahoma historyāš—ļø physical sciencešŸŽ™ļø speech and debatešŸ¤ texas government🤠 texas history🌲 washington state historyšŸ•Šļø world religions
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APĀ® and SATĀ® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.