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  • AS LevelExpand
    • Pure 1Expand
      • 1.1 QuadraticsExpand
        • 1.1.1 Completing the Square
        • 1.1.2 The Discriminant
        • 1.1.3 Solving Quadratic Equations
        • 1.1.4 Solving Quadratic Inequalities
        • 1.1.5 Solving Simultaneous Equations
        • 1.1.6 Hidden Quadratics
      • 1.2 FunctionsExpand
        • 1.2.1 Definitions and Range of a Function
        • 1.2.2 Inverse of a Function
        • 1.2.3 Transformations
      • 1.3 Coordinate geometryExpand
        • 1.3.1 Equation of a Straight Line
        • 1.3.2 Equation of a Circle
      • 1.4 Circular measureExpand
        • 1.4.1 Circular Measure
      • 1.5 TrigonometryExpand
        • 1.5.1 Trigonometric Functions and their Transformations
        • 1.5.2 Solving Trigonometric Equations
        • 1.5.3 Trigonometric Identities
      • 1.6 SeriesExpand
        • 1.6.1 Binomial Expansion
        • 1.6.2 Arithmetic Progressions
        • 1.6.3 Geometric Progressions
        • 1.6.4 Arithmetic and Geometric Progressions Combined
      • 1.7 DifferentiationExpand
        • 1.7.1 Basic Differentiation
        • 1.7.2 Tangents and Normals
        • 1.7.3 Increasing and Decreasing Functions
        • 1.7.4 Rates of Change
        • 1.7.5 Locating and Determining the Nature of Stationary Points
      • 1.8 IntegrationExpand
        • 1.8.1 Basics of Integration
        • 1.8.2 Area Under the Graph
        • 1.8.3 Volume of Revolution
    • Statistics 1Expand
      • 5.1 Representation of DataExpand
        • 5.1.1 Advantages and Disadvantages of Representation of Data
        • 5.1.2 Stem and Leaf Diagrams
        • 5.1.3 Box and Whisker Plots
        • 5.1.4 Histograms
        • 5.1.5 Cumulative Frequency Graphs
        • 5.1.6 Measures of Central Tendency and Variation
        • 5.1.7 Coded Data
      • 5.2 Permutations and CombinationsExpand
        • 5.2.1 Arrangements
        • 5.2.2 Permutations
        • 5.2.3 Combinations
      • 5.3 ProbabilityExpand
        • 5.3.1 Evaluating Probabilities in Simple Cases
        • 5.3.2 Exclusive and Independent Events
        • 5.3.3 Tree Diagrams and Conditional Probability
      • 5.4 Discrete Random VariablesExpand
        • 5.4.1 The Probability Distribution Table
        • 5.4.2 The Binomial Distribution
        • 5.4.3 The Geometric Distribution
      • 5.5 The Normal DistributionExpand
        • 5.5.1 Basics of the Normal Distribution
        • 5.5.2 Finding Mean and Standard Deviation
        • 5.5.3 Normal Approximation to the Binomial Distribution
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      • 3.1 AlgebraExpand
        • 3.1.1 The Modulus Function
        • 3.1.2 Polynomial Division, Factor Theorem and Remainder Theorem
        • 3.1.3 Partial Fractions
        • 3.1.4 Binomial Expansion
      • 3.2 Logarithmic and Exponential FunctionsExpand
        • 3.2.1 Logarithmic and Exponential Functions
        • 3.2.2 Linear Law (reduction of an equation to linear form)
      • 3.3 TrigonometryExpand
        • 3.3.1 Trigonometry
      • 3.4 DifferentiationExpand
        • 3.4.1 Differentiation
      • 3.5 IntegrationExpand
        • 3.5.1 Integration of Exponentials, Rational and Trigonometric Functions
        • 3.5.2 Rational Functions to Partial Fractions and Method of Recognition
        • 3.5.3 Integration by parts
        • 3.5.4 Integration by Substitution
      • 3.6 Numerical Solution of EquationsExpand
        • 3.6.1 Numerical Solution of Equations
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        • 3.7.1 Basics of Vectors
        • 3.7.2 Vector Equation of a Straight Line
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        • 3.7.4 Scalar Product and its Applications
      • 3.8 Differential EquationsExpand
        • 3.8.1 Differential Equations
      • 3.9 Complex NumbersExpand
        • 3.9.1 Basics of Complex Numbers
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        • 3.9.3 Polar Form
        • 3.9.4 The Two Square Roots of a Complex Number
        • 3.9.5 Argand Diagrams
    • Statistics 2Expand
      • 6.1 The Poisson DistributionExpand
        • 6.1.1 The Poisson Distribution
      • 6.2 Linear Combinations of Random VariablesExpand
        • 6.2.1 Linear Combinations of Random Variables
      • 6.3 Continuous Random VariablesExpand
        • 6.3.1 Continuous Random Variables
      • 6.4 Sampling and EstimationExpand
        • 6.4.1 Random Sampling, Sample Mean and The Central Limit Theorem
        • 6.4.2 Unbiased Estimates of Population Mean and Variance
        • 6.4.3 Confidence Intervals
      • 6.5 Hypothesis TestsExpand
        • 6.5.1 Normal Distribution Tests
        • 6.5.2 Discrete Tests
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Home / AS Level / 1.8.2 Area Under the Graph

1.8.2 Area Under the Graph

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1.8.1 Basics of Integration
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1.8.3 Volume of Revolution

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  • AS Level
    • Pure 1
      • 1.1 Quadratics
        • 1.1.1 Completing the Square
        • 1.1.2 The Discriminant
        • 1.1.3 Solving Quadratic Equations
        • 1.1.4 Solving Quadratic Inequalities
        • 1.1.5 Solving Simultaneous Equations
        • 1.1.6 Hidden Quadratics
      • 1.2 Functions
        • 1.2.1 Definitions and Range of a Function
        • 1.2.2 Inverse of a Function
        • 1.2.3 Transformations
      • 1.3 Coordinate geometry
        • 1.3.1 Equation of a Straight Line
        • 1.3.2 Equation of a Circle
      • 1.4 Circular measure
        • 1.4.1 Circular Measure
      • 1.5 Trigonometry
        • 1.5.1 Trigonometric Functions and their Transformations
        • 1.5.2 Solving Trigonometric Equations
        • 1.5.3 Trigonometric Identities
      • 1.6 Series
        • 1.6.1 Binomial Expansion
        • 1.6.2 Arithmetic Progressions
        • 1.6.3 Geometric Progressions
        • 1.6.4 Arithmetic and Geometric Progressions Combined
      • 1.7 Differentiation
        • 1.7.1 Basic Differentiation
        • 1.7.2 Tangents and Normals
        • 1.7.3 Increasing and Decreasing Functions
        • 1.7.4 Rates of Change
        • 1.7.5 Locating and Determining the Nature of Stationary Points
      • 1.8 Integration
        • 1.8.1 Basics of Integration
        • 1.8.2 Area Under the Graph
        • 1.8.3 Volume of Revolution
    • Statistics 1
      • 5.1 Representation of Data
        • 5.1.1 Advantages and Disadvantages of Representation of Data
        • 5.1.2 Stem and Leaf Diagrams
        • 5.1.3 Box and Whisker Plots
        • 5.1.4 Histograms
        • 5.1.5 Cumulative Frequency Graphs
        • 5.1.6 Measures of Central Tendency and Variation
        • 5.1.7 Coded Data
      • 5.2 Permutations and Combinations
        • 5.2.1 Arrangements
        • 5.2.2 Permutations
        • 5.2.3 Combinations
      • 5.3 Probability
        • 5.3.1 Evaluating Probabilities in Simple Cases
        • 5.3.2 Exclusive and Independent Events
        • 5.3.3 Tree Diagrams and Conditional Probability
      • 5.4 Discrete Random Variables
        • 5.4.1 The Probability Distribution Table
        • 5.4.2 The Binomial Distribution
        • 5.4.3 The Geometric Distribution
      • 5.5 The Normal Distribution
        • 5.5.1 Basics of the Normal Distribution
        • 5.5.2 Finding Mean and Standard Deviation
        • 5.5.3 Normal Approximation to the Binomial Distribution
  • A Level
    • Pure 3
      • 3.1 Algebra
        • 3.1.1 The Modulus Function
        • 3.1.2 Polynomial Division, Factor Theorem and Remainder Theorem
        • 3.1.3 Partial Fractions
        • 3.1.4 Binomial Expansion
      • 3.2 Logarithmic and Exponential Functions
        • 3.2.1 Logarithmic and Exponential Functions
        • 3.2.2 Linear Law (reduction of an equation to linear form)
      • 3.3 Trigonometry
        • 3.3.1 Trigonometry
      • 3.4 Differentiation
        • 3.4.1 Differentiation
      • 3.5 Integration
        • 3.5.1 Integration of Exponentials, Rational and Trigonometric Functions
        • 3.5.2 Rational Functions to Partial Fractions and Method of Recognition
        • 3.5.3 Integration by parts
        • 3.5.4 Integration by Substitution
      • 3.6 Numerical Solution of Equations
        • 3.6.1 Numerical Solution of Equations
      • 3.7 Vectors
        • 3.7.1 Basics of Vectors
        • 3.7.2 Vector Equation of a Straight Line
        • 3.7.3 Parallel, Intersect or Skew Lines
        • 3.7.4 Scalar Product and its Applications
      • 3.8 Differential Equations
        • 3.8.1 Differential Equations
      • 3.9 Complex Numbers
        • 3.9.1 Basics of Complex Numbers
        • 3.9.2 Solving Polynomial Equations with Complex Roots
        • 3.9.3 Polar Form
        • 3.9.4 The Two Square Roots of a Complex Number
        • 3.9.5 Argand Diagrams
    • Statistics 2
      • 6.1 The Poisson Distribution
        • 6.1.1 The Poisson Distribution
      • 6.2 Linear Combinations of Random Variables
        • 6.2.1 Linear Combinations of Random Variables
      • 6.3 Continuous Random Variables
        • 6.3.1 Continuous Random Variables
      • 6.4 Sampling and Estimation
        • 6.4.1 Random Sampling, Sample Mean and The Central Limit Theorem
        • 6.4.2 Unbiased Estimates of Population Mean and Variance
        • 6.4.3 Confidence Intervals
      • 6.5 Hypothesis Tests
        • 6.5.1 Normal Distribution Tests
        • 6.5.2 Discrete Tests
        • 6.5.3 Type I and Type II errors

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  • Home
  • Shop
  • Tutoring
  • Topical Questions
  • Guess Papers
  • AS Level
    • Pure 1
      • 1.1 Quadratics
        • 1.1.1 Completing the Square
        • 1.1.2 The Discriminant
        • 1.1.3 Solving Quadratic Equations
        • 1.1.4 Solving Quadratic Inequalities
        • 1.1.5 Solving Simultaneous Equations
        • 1.1.6 Hidden Quadratics
      • 1.2 Functions
        • 1.2.1 Definitions and Range of a Function
        • 1.2.2 Inverse of a Function
        • 1.2.3 Transformations
      • 1.3 Coordinate geometry
        • 1.3.1 Equation of a Straight Line
        • 1.3.2 Equation of a Circle
      • 1.4 Circular measure
        • 1.4.1 Circular Measure
      • 1.5 Trigonometry
        • 1.5.1 Trigonometric Functions and their Transformations
        • 1.5.2 Solving Trigonometric Equations
        • 1.5.3 Trigonometric Identities
      • 1.6 Series
        • 1.6.1 Binomial Expansion
        • 1.6.2 Arithmetic Progressions
        • 1.6.3 Geometric Progressions
        • 1.6.4 Arithmetic and Geometric Progressions Combined
      • 1.7 Differentiation
        • 1.7.1 Basic Differentiation
        • 1.7.2 Tangents and Normals
        • 1.7.3 Increasing and Decreasing Functions
        • 1.7.4 Rates of Change
        • 1.7.5 Locating and Determining the Nature of Stationary Points
      • 1.8 Integration
        • 1.8.1 Basics of Integration
        • 1.8.2 Area Under the Graph
        • 1.8.3 Volume of Revolution
    • Statistics 1
      • 5.1 Representation of Data
        • 5.1.1 Advantages and Disadvantages of Representation of Data
        • 5.1.2 Stem and Leaf Diagrams
        • 5.1.3 Box and Whisker Plots
        • 5.1.4 Histograms
        • 5.1.5 Cumulative Frequency Graphs
        • 5.1.6 Measures of Central Tendency and Variation
        • 5.1.7 Coded Data
      • 5.2 Permutations and Combinations
        • 5.2.1 Arrangements
        • 5.2.2 Permutations
        • 5.2.3 Combinations
      • 5.3 Probability
        • 5.3.1 Evaluating Probabilities in Simple Cases
        • 5.3.2 Exclusive and Independent Events
        • 5.3.3 Tree Diagrams and Conditional Probability
      • 5.4 Discrete Random Variables
        • 5.4.1 The Probability Distribution Table
        • 5.4.2 The Binomial Distribution
        • 5.4.3 The Geometric Distribution
      • 5.5 The Normal Distribution
        • 5.5.1 Basics of the Normal Distribution
        • 5.5.2 Finding Mean and Standard Deviation
        • 5.5.3 Normal Approximation to the Binomial Distribution
  • A Level
    • Pure 3
      • 3.1 Algebra
        • 3.1.1 The Modulus Function
        • 3.1.2 Polynomial Division, Factor Theorem and Remainder Theorem
        • 3.1.3 Partial Fractions
        • 3.1.4 Binomial Expansion
      • 3.2 Logarithmic and Exponential Functions
        • 3.2.1 Logarithmic and Exponential Functions
        • 3.2.2 Linear Law (reduction of an equation to linear form)
      • 3.3 Trigonometry
        • 3.3.1 Trigonometry
      • 3.4 Differentiation
        • 3.4.1 Differentiation
      • 3.5 Integration
        • 3.5.1 Integration of Exponentials, Rational and Trigonometric Functions
        • 3.5.2 Rational Functions to Partial Fractions and Method of Recognition
        • 3.5.3 Integration by parts
        • 3.5.4 Integration by Substitution
      • 3.6 Numerical Solution of Equations
        • 3.6.1 Numerical Solution of Equations
      • 3.7 Vectors
        • 3.7.1 Basics of Vectors
        • 3.7.2 Vector Equation of a Straight Line
        • 3.7.3 Parallel, Intersect or Skew Lines
        • 3.7.4 Scalar Product and its Applications
      • 3.8 Differential Equations
        • 3.8.1 Differential Equations
      • 3.9 Complex Numbers
        • 3.9.1 Basics of Complex Numbers
        • 3.9.2 Solving Polynomial Equations with Complex Roots
        • 3.9.3 Polar Form
        • 3.9.4 The Two Square Roots of a Complex Number
        • 3.9.5 Argand Diagrams
    • Statistics 2
      • 6.1 The Poisson Distribution
        • 6.1.1 The Poisson Distribution
      • 6.2 Linear Combinations of Random Variables
        • 6.2.1 Linear Combinations of Random Variables
      • 6.3 Continuous Random Variables
        • 6.3.1 Continuous Random Variables
      • 6.4 Sampling and Estimation
        • 6.4.1 Random Sampling, Sample Mean and The Central Limit Theorem
        • 6.4.2 Unbiased Estimates of Population Mean and Variance
        • 6.4.3 Confidence Intervals
      • 6.5 Hypothesis Tests
        • 6.5.1 Normal Distribution Tests
        • 6.5.2 Discrete Tests
        • 6.5.3 Type I and Type II errors
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