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Integrals

Learning tasks
                      
Lesson Summary
Text book
Exercises Correction
A) The Definite Integral as an Area
    I) Approximating Area with Riemann Sums
      1) Estimating Area with Left and Right SumsEx 1 Ex 2 Ex 3
    II) Definition of the Definite Integral
      2) Identifying the Definite Integral for a Given AreaEx 4 Ex 5 Ex 6 Ex 7
      3) Interpreting the Sign of a Definite IntegralEx 8 Ex 9 Ex 10 Ex 11
      4) Evaluating Integrals using Geometric FormulasEx 12 Ex 13 Ex 14 Ex 15
    III) Properties of the Definite Integral
      5) Applying the Properties of Definite IntegralsEx 16 Ex 17 Ex 18 Ex 19 Ex 20
B) The Fundamental Theorem of Calculus
    I) Antiderivatives
      6) Verifying Antiderivatives by DifferentiationEx 21 Ex 22 Ex 23 Ex 24
      7) Finding Antiderivatives by InspectionEx 25 Ex 26 Ex 27 Ex 28
    II) Finding Antiderivatives
      8) Finding Antiderivatives of Basic FunctionsEx 29 Ex 30 Ex 31 Ex 32 Ex 33 Ex 34
      9) Applying the Linearity of IntegrationEx 35 Ex 36 Ex 37 Ex 38 Ex 39
      10) Applying the Reverse Chain RuleEx 40 Ex 41 Ex 42 Ex 43
      11) Finding a Specific Antiderivative using an Initial ConditionEx 44 Ex 45 Ex 46
    III) Fundamental Theorem of Calculus
      12) Calculating Area using the Fundamental TheoremEx 47 Ex 48 Ex 49
      13) Evaluating Definite Integrals: Level 1Ex 50 Ex 51 Ex 52 Ex 53
      14) Evaluating Definite Integrals: Level 2Ex 54 Ex 55 Ex 56 Ex 57
      15) Defining Functions using Definite IntegralsEx 58 Ex 59 Ex 60
      16) Proving the Properties of Definite IntegralsEx 61 Ex 62 Ex 63 Ex 64 Ex 65
      17) Studying Sequences Defined by IntegralsEx 66 Ex 67 Ex 68
C) Techniques for Integration
    I) Integration by Reverse Chain Rule
      18) Finding Integrals from DerivativesEx 69 Ex 70 Ex 71 Ex 72
    II) Integration by Substitution
      19) Integrating by Substitution for Indefinite IntegralsEx 73 Ex 74 Ex 75 Ex 76
      20) Evaluating Definite Integrals by SubstitutionEx 77 Ex 78 Ex 79 Ex 80
    III) Integration by Parts
      21) Evaluating Definite Integrals by PartsEx 81 Ex 82 Ex 83 Ex 84
      22) Applying Advanced Integration TechniquesEx 85 Ex 86 Ex 87 Ex 88