Math 12
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3.1 Introduction
3.1 Introduction
3.1.1 Differentials of Variables
3.1.2 Distinguishing Between dy and delta-y
3.1.3 Finding dy/dx by using differentials
3.1.4 Simple application of differentials
Exercise 3.1
3.2 Integration as Anti Derivative (Inverse of Derivative)
3.2 Integration as Anti Derivative (Inverse of Derivative)
3.2.1 Some Standard Formulae for Anti Derivatives
3.2.2 Theorems on Anti Derivatives
3.2.3 Anti-Derivatives of [f(x)]n f ’(x) and [f(x)]-1 f ’(x)
Exercise 3.2
3.3 Integration by Method of Substitution
3.4 Some useful Substitutions
Exercise 3.3
3.5 Integration by parts
Exercise 3.4
3.5 Integration involving partial Fractions
Exercise 3.5
3.6 The Definite Integrals
3.6 The Definite Integrals
3.6.1 The Area Under The Curve
3.6.2 Fundamental Theorem and Properties of Definite Integrals
Exercise 3.6
3.7 Application of Definite integrals
Exercise 3.7
3.8 Differential Equations
3.8 Differential Equations
3.8.1 Solution of a Differential Equation of first order
3.8.2 Initial Conditions
Exercise 3.8
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