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      • Unit 0 - Simultaneous Equations
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      • Unit 18 - Volumes and Surface Area
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      • Unit 20 - Logarithms
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  • IB
    • Mathematical Studies >
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        • Unit 1 - Number Review
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      • HL Unit Resources >
        • Unit 1 - Algebra
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      • AASL Unit Resources >
        • Unit 0 - Proof
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        • Unit 4 - Exponentials and Logarithms
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        • Unit 10 - Differentiation 2
        • Unit 11 - Integration
      • AASL Revision Materials
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Unit 8 - Integral Calculus

Unit Objectives
Prior Knowledge:
  •  Differential Calculus
By the end of this unit students should be able to:
  • Understand indefinite integration as anti-differentiation
  • Integrate polynomials, sine, cosine and the exponential function
  • Integrate using the reverse of known differential results
  • Integrate with boundary conditions to determine the constant of integration
  • Integrate with limits (definite integration)
  • Determine areas between curves and the x and y axes and areas enclosed between curves
  • Find volumes of revolution about the x and y axes.
  • Integrate by substitution
  • Integrate by parts
  • Solve problems of kinematics
Lesson Resources​
0. Unit Map
Unit Map
1. Anti-Differentiation
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Worksheet
2. Constants of Integration
Lesson Sheet
Lesson Sheet COMPLETE
3. Indefinite Integration
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
4. Equations of Curves
Lesson Sheet
Lesson Sheet COMPLETE
5. Reverse Chain Rule
Lesson Sheet
Lesson Sheet COMPLETE
6. Definite Integration
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Worksheet
7. Geometric Significance
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Autograph Activity
Autograph Activity
8. Properties of Definite Integrals
Lesson Sheet
Lesson Sheet COMPLETE
9. Area to y-axis
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Autograph Activity
Worksheet
10. Area Between Curves
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Autograph Activity
Worksheet
11. Further Integration and Trigonometry
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
12. Integration By Substitution
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
13. Special Substitutions
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
14. Integration By Parts
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
2500+ Integrals Worksheet
15. ​Volumes of Revolution
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
Investigation
16. Kinematics
Lesson Sheet
Lesson Sheet COMPLETE
Lesson
For a whole range of mathematical activities for use in and out of the classroom, including random question generators, Bingo generators and worksheet generators, as well as computer based investigations and activities check out my main site: www.interactive-maths.com.

​If you are interested in codes, ciphers and codebreaking, then check out my secondary site, Crypto Corner, dedicated to providing information about all types of ciphers, as well as tools for encrypting, decrypting and breaking messages.
  • Home
  • IGCSE
    • IGCSE Unit Resources >
      • Unit 0 - Simultaneous Equations
      • Unit 0 - Regression
      • Unit 1 - Percentages
      • Unit 2 - Sets
      • Unit 2 - Graphs and GDC
      • Unit 3 - Indices and Surds
      • Unit 4 - Circle Theorems
      • Unit 5 - Formulae
      • Unit 6 - Vectors
      • Unit 7 - Quadratic Equations
      • Unit 8 - Tree Diagrams
      • Unit 9 - Coordinate Geometry
      • Unit 10 - Sequences
      • Unit 11 - Statistical Diagrams
      • Unit 12 - Composite and Inverse Functions
      • Unit 13 - Similarity
      • Unit 14 - Variation
      • Unit 15 - Algebraic Fractions
      • Unit 16 - Advanced Trigonometry
      • Unit 17 - Quadratic Functions
      • Unit 18 - Volumes and Surface Area
      • Unit 19 - Graphs
      • Unit 20 - Logarithms
      • Unit 21 - Transforming Graphs
    • IGCSE Revision Materials
  • IB
    • Mathematical Studies >
      • MSSL Unit Resources >
        • Unit 1 - Number Review
        • Unit 2 - Sequences and Series
        • Unit 3 - Statistics 1
        • Unit 4 - Functions 1
        • Unit 5 - Trigonometry and Mensurations
        • Unit 6 - Functions 2
        • Unit 7 - Statistics 2
        • Unit 8 - Differentiation
        • Unit 9 - Sets and Probability
        • Unit 10 - Functions 3
        • Unit 11 - Financial Maths
        • Unit 12 - Statistics 3
        • Unit 13 - Logic
      • IB Studies Revision Homework
      • MSSL Revision Materials
      • Studies Exam Question Practice
    • Mathematics Higher Level >
      • HL Unit Resources >
        • Unit 1 - Algebra
        • Unit 2 - Functions & Equations
        • Unit 3 - Trigonometry
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Statistics and Probability
        • Unit 6 - Differential Calculus
        • Unit 7 - Discrete Probability Distributions
        • Unit 8 - Integral Calculus
        • Unit 9 - Continuous Probability Distributions
        • Unit 10 - Complex Numbers
        • Unit 11A - Statistics Option
        • Unit 11B - Sets and Groups Option
        • Unit 12 - Vectors
      • HL Revision Materials >
        • HL Weekly Quizzes
    • Mathematics AA SL >
      • AASL Unit Resources >
        • Unit 0 - Proof
        • Unit 1 - Algebra Functions Basics
        • Unit 2 - Functions, Equations and Inequalities
        • Unit 3 - Sequences and Series
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Trigonometric Functions and Equations
        • Unit 6 - Differentiation 1
        • Unit 7 - Statistics
        • Unit 8 - Probability
        • Unit 9 - Mensuration
        • Unit 10 - Differentiation 2
        • Unit 11 - Integration
      • AASL Revision Materials
      • AASL Key Skills Generator