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Spherical Volume (2 of 2: Derivation of the Volume of a Sphere through Solids of Revolution)
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Classroom Contents
Applications of Calculus
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- 1 Maximum & Minimum
- 2 Turning Points
- 3 Stationary Points
- 4 Non-Stationary Turning Points (1 of 2)
- 5 Non-Stationary Turning Points (2 of 2)
- 6 Introduction to Points of Inflexion
- 7 The Special Case of x^4
- 8 Horizontal Points of Inflexion
- 9 Overview of Critical Points (1 of 2)
- 10 Overview of Critical Points (2 of 2)
- 11 Overview of Critical Points: Examples (1 of 2)
- 12 Overview of Critical Points: Examples (2 of 2)
- 13 Finding and Confirming Turning Points
- 14 Curve Sketching: Locating Stationary Points
- 15 Curve Sketching: Determining Nature of SPs
- 16 Curve Sketching: Drawing the Graph
- 17 Sign of the First Derivative
- 18 Second Derivative: A Physical Analogy
- 19 Second Derivative: Concavity
- 20 Second Derivative: Notation
- 21 Second Derivative: Relationship w/ First Derivative
- 22 Graphing w/ the First Derivative
- 23 Graphing w/ the Second Derivative
- 24 Choosing First or Second Derivative
- 25 Graph Behaviour Chart
- 26 Implicit Differentiation
- 27 Implicit Differentiation - example question
- 28 Visual Approach to Derivatives (1 of 2)
- 29 Visual Approach to Derivatives (2 of 2)
- 30 Y11 Mathematics Ext 1 Quiz (1 of 2: Curve sketching with calculus)
- 31 Introduction to Solids of Revolution
- 32 Verifying Formulae for Cylinder, Cone & Sphere
- 33 Compound Volumes (1 of 2)
- 34 Compound Volumes (2 of 2)
- 35 Volumes: Examples around x-axis & y-axis
- 36 Subtraction of Volumes
- 37 Subtraction of Volumes: Class Discussion
- 38 Volume within a Cone (1 of 3: Separating variables and constants for differentiation)
- 39 Volume within a Cone (2 of 3: Finding Volume in terms of a single variable to differentiate)
- 40 Volume within a Cone (3 of 3: Finding the Stationary Points to determine the maximum volume)
- 41 Solids of Revolution (1 of 3: What happens when you rotate an area around an axis?)
- 42 Solid of Revolution (2 of 3: Finding Volume of the Solid of Revolution using Volume of a cylinder)
- 43 Solids of Revolution (3 of 3: Finding the Volume of an area rotated around the y axis)
- 44 Conical Volume (1 of 2: Derivation of the Volume of a Cone through Solids of Revolution)
- 45 Spherical Volume (2 of 2: Derivation of the Volume of a Sphere through Solids of Revolution)
- 46 Difference between Volumes (1 of 2: Method to finding the difference between volumes)
- 47 Difference Between Volumes (2 of 2: Investigating the relationship between Parabolas & Cylinders)
- 48 Intro to Solids of Revolution (1 of 3: Establishing the formula)
- 49 Intro to Solids of Revolution (2 of 3: Simple worked example)
- 50 Intro to Solids of Revolution (3 of 3: Other axes, volume of a sphere)
- 51 Solids of Revolution - Subtracting Volumes
- 52 Non-Standard Integrals: "Differentiate, hence integrate" (1 of 2)
- 53 Non-Standard Integrals: "Differentiate, hence integrate" (2 of 2)
- 54 Areas Under Curves: Logarithmic Functions
- 55 Integration & Logarithmic Functions: Log Integrands (1 of 2)
- 56 Integration & Logarithmic Functions: Log Integrands (2 of 2)
- 57 Integration & Logarithmic Functions: Non-Log Integrands (1 of 3)
- 58 Integration & Logarithmic Functions: Non-Log Integrands (2 of 3)
- 59 Integration & Logarithmic Functions: Non-Log Integrands (3 of 3)
- 60 Areas Under Curves: Logarithmic Functions (Alternative Approach)
- 61 Applications & Implications of d/dx(½v²): Concrete Example
- 62 Motion Exam Question (1 of 2: Finding v(x) from a(x))
- 63 Motion Exam Question (2 of 2: Finding x(t) from v(x))
- 64 Differentiating x^x (3 of 3: Implicit Differentiation)
- 65 Implicit Differentiation (Differentiating a function without needing to rearrange for x or y)
- 66 Rates of Change (1 of 4: Finding the Volume of an unknown height of water with a diagram)
- 67 Maximum/Minimum with Quadratics (1 of 2: Axis of symmetry)
- 68 Maximum/Minimum with Quadratics (2 of 2: Completing the square)
- 69 Max/Min Question: Cutting a Wire in Two (1 of 2: Setting up the equations)
- 70 Max/Min Question: Cutting a Wire in Two (2 of 2: Finding the minimum)
- 71 Challenging Max/Min Exam Question
- 72 Graphing Logarithmic Function with Calculus (1 of 2: Identifying features)
- 73 Graphing Logarithmic Function with Calculus (2 of 2: Constructing the sketch)
- 74 Differential Equation in terms of Dependent Variable (1 of 2: Partial Fractions)
- 75 Differential Equation in terms of Dependent Variable (2 of 2: Integration)
