C6: Techniques of Integration

C6: Techniques of Integration

1. 1: Integration by Substitution

   • 1.1: Indefinite Integrals
   • 1.2: Definite Integrals

2. 2: Integration by parts

   • 2.1: Indefinite Integrals
   • 2.2: Definite Integrals
   • 2.3: Strategy for applying Integration by parts
   • 2.4: Special case
   • 2.5: Other Examples

3. 3: Integration using Partial Fractions

   • 3.1: Polynomial Long Division
   • 3.2: Partial Fractions
     • Completing the square
     • Partial Fraction Decomposition

4. 4: Trigonometric Integrals

   • 4.1: Pythagorean Identities
   • 4.2: Squared Integrands
   • 4.3: Double Angle Identities
   • 4.4: Logarithmic Forms
   • 4.5: Rational Functions
   • 4.6: Other Cases
   • 4.7: Products of cos and sin
   • 4.8: Hyperbolic Identities

5. 5: Trigonometric Substitution

   • 5.1??? Long proofs
   • 5.1: Hyperbolic Substitution

6. 6: Improper Integrals

   • 6.1: Integrating over Unbounded Intervals
   • 6.2:Integrating Unbounded Integrands
   • 6.3: Improper Integral of Power Functions
   • 6.4: Hadamard's Pricipal Part
   • 6.5: Comparison Test for Improper Integrals

7. 7: Solids of Revolution

   • 7.1: Volumes by Discs
   • 7.2: Volumes by Shells