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Integrals

Learning tasks
                  
Lesson Summary
Text book
Exercises Correction
A) The Definite Integral as an Area
    I) Definition of the Definite Integral
      1) Identifying the Definite Integral for a Given AreaEx 1 Ex 2 Ex 3 Ex 4
      2) Interpreting the Sign of a Definite IntegralEx 5 Ex 6 Ex 7 Ex 8
      3) Evaluating Integrals using Geometric FormulasEx 9 Ex 10 Ex 11 Ex 12
    II) Properties of the Definite Integral
      4) Applying the Properties of Definite IntegralsEx 13 Ex 14 Ex 15 Ex 16 Ex 17
B) The Fundamental Theorem of Calculus
    I) Antiderivatives
      5) Verifying Antiderivatives by DifferentiationEx 18 Ex 19 Ex 20 Ex 21
      6) Finding Antiderivatives by InspectionEx 22 Ex 23 Ex 24 Ex 25
    II) Finding Antiderivatives
      7) Finding Antiderivatives of Basic FunctionsEx 26 Ex 27 Ex 28 Ex 29 Ex 30 Ex 31
      8) Applying the Linearity of IntegrationEx 32 Ex 33 Ex 34 Ex 35 Ex 36
      9) Applying the Reverse Chain RuleEx 37 Ex 38 Ex 39 Ex 40
      10) Finding a Specific Antiderivative using an Initial ConditionEx 41 Ex 42 Ex 43
    III) Fundamental Theorem of Calculus
      11) Calculating Area using the Fundamental TheoremEx 44 Ex 45 Ex 46
      12) Evaluating Definite Integrals: Level 1Ex 47 Ex 48 Ex 49 Ex 50
      13) Evaluating Definite Integrals: Level 2Ex 51 Ex 52 Ex 53 Ex 54
      14) Defining Functions using Definite IntegralsEx 55 Ex 56 Ex 57
      15) Studying Sequences Defined by IntegralsEx 58 Ex 59 Ex 60
C) Techniques for Integration
    I) Integration by Reverse Chain Rule
      16) Finding Integrals from DerivativesEx 61 Ex 62 Ex 63 Ex 64
    II) Integration by Substitution
      17) Integrating by Substitution for Indefinite IntegralsEx 65 Ex 66 Ex 67 Ex 68
      18) Evaluating Definite Integrals by SubstitutionEx 69 Ex 70 Ex 71 Ex 72