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Term 9 · Year 3

Term 9 — Integral Calculus

Antiderivative, definite integral, FTC, techniques, applications.

10 lessons  ·  10 published ·  ~32h of study

(Year 3 — Integral, ODEs, Inference, Linear Algebra)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Antiderivative, definite integral and FTC

~9h · 3 lessons
  1. Lesson 81
    Antiderivative and indefinite integral
    F'(x) = f(x), indefinite integral notation
    published →
  2. Lesson 82
    Definite integral and oriented area
    ∫ₐᵇ f(x) dx as Riemann sum limit
    published →
  3. Lesson 83
    Fundamental Theorem of Calculus
    FTC parts 1 and 2, applications
    published →

Class B — Substitution, integration by parts, partial fractions

~9h · 3 lessons
  1. Lesson 84
    Technique: u-substitution
    u-substitution, change of variables
    published →
  2. Lesson 85
    Integration by Parts
    ∫ u dv = uv - ∫ v du, LIATE
    published →
  3. Lesson 86
    Integrals of rational functions (partial fractions)
    Partial fraction decomposition, rational functions
    published →

Class C — Trigonometric integrals

~3h · 1 lessons
  1. Lesson 87
    Trigonometric integrals and trigonometric substitution
    ∫ sin^n cos^m, ∫ sec^n tan^m, identities
    published →

Class D — Area, volume + synthesis

~9h · 3 lessons
  1. Lesson 88
    Area between curves
    Area between two curves, integration along y
    published →
  2. Lesson 89
    Volume by slicing: disks, washers, and cylindrical shells
    Disk method, shell method, revolution solids
    published →
  3. Lesson 90
    Term 9 Consolidation (integral calculus)
    Synthesis: 60 mixed integral problems
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 9 →