Integration

Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore.

• Introduction
  • Differentials of Variables
  • Distinguishing Between dy and δy
  • Simple application of Differentials
  • Exercise 3.1
• Integration as anti-derivative ( Inverse of Derivative)
  • Some Standrad Formulae for Anti-Derivatives
  • Theorems on Anti Derivatives
  • Anti-Derivatives of [f(x)]nf′(x) and [f(x)]−1f′(x)
  • Exercise 3.2
• Integration by Method of Substitution
• Some Useful Substitutions
  • Exercise 3.3
• Integration by parts
  • Exercise 3.4
• Integration involving Partial Fraction
  • Exercise 3.5
• The Definite Integrals
  • The Area Under the Curve
  • Theorem of Integrals
  • Exercise 3.6
• Application of Definite Integrals
  • Exercise 3.7
• Differential Equations
• Solution of a Differential Equation of First Order
• Initial Conditions
• Exercise 3.8

• Exercise 3.1
• Exercise 3.2