Mathematics for Management -- Supplementary Electronic Materials

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The Fundamental Theorem of Calculus

 
The Fundamental Theorem of Calculus -- Structure
 
Antiderivatives & Indefinite Integrals
 

Indefinite Integration

The contents of this unit include:
  • The definition of antidifferentiation or indefinite integration
  • The indefinite integral is a family of functions
  • Verifying an antiderivative
  • Fundamental properties of antiderivatives
  • Sketching the graph of an antiderivative
  • Rectlinear motion
video clip slides knowledge quiz
 

Integration yielding Inverse Trigonometric Functions

The contents of this unit include:
  • Implicit differentiation of inverse trigonometric functions
  • Interpretation of antiderivatives of certain functions as inverse trigonometric functions
video clip slides knowledge quiz
 

First Rules of Integration

The contents of this unit include:
  • Reversing analogous differentiation rules: constant rule, power rule, logarithmic rule, exponential rule
  • Algebraic rules: Constant multiple rule, sum/ difference rule
  • Summary of antidifferentiation formulas
video clip slides knowledge quiz
 

Worked-Out Exercises

worked out exercises
 
Advanced Integration Rules
 

The Substitution Rule

The contents of this unit include:
  • The substitution rule of integration as the reverse of the chain rule of differentiation
  • Application of the substitution rule for determining indefinite integrals
video clip slides knowledge quiz
 

Definite Integrals

The contents of this unit include:
  • Definite integrals of functions \( f(x) \geq 0 \) as areas between the graph of \( f(x) \) and the \(x\)-axis
  • Riemann sum approximation
  • The value of a definite integral is the limit for infinite interval partitions of the corresponding Riemann sum approximation
  • The definite integral is a specific number
video clip slides knowledge quiz
 

The Fundamental Theorem of Calculus

The contents of this unit include:
  • Connecting indefinite integrals (i.e. a family of functions) with definite integrals (i.e. a specific number)
  • The Fundamental Theorem of Calculus
  • Justification of the Fundamental Theorem of Calculus
  • Computation rules for definite integrals: constant multiple rule, sum/ difference rule, one point evaluation, reversed boundaries, subdivision rule
  • The Net Change Theorem
video clip slides knowledge quiz
 

Worked-Out Exercises

worked out exercises
 
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