Technique of Intergral

Technique of Intergral

1. ·

   • Basic Substitution
     • Choose U
       • Find dU
         • Subs

2. ·

   • Completing the square

3. ·

   • Trigonometric Identities

4. ·

   • Use Identities

5. ·

   • Improper Fraction
     • Degree numerator > enominator
       • Long Division Method

6. ·

   • Separating Fraction
     • numerator only

7. ·

   • Multiplying form of 1

8. ·

   • Eliminate square root

9. ·

   • Integration by Parts
     • {u dv
       • Use I, L, A, T, E
         • Find du and v
           • Formula
     • Tubular Integration
       • Choose U
         • must differentiable until 0
           • Example

10. ·

    • Intergration by Partial Fraction
      • Improper fraction
        • Long Division Method
          • Use CoverUp method
      • Rational fraction
        • Factorise denominator

11. ·

    • Power trigo >2
      • Trigonometric Integrals
        • 1 term
          • • manipulate until power 2
            • Reduction Formula
              • Formula
        • 2 term
          • both odd
            • • choose lower power
          • both even
            • • Manipulate until power 2
          • 1 even 1 odd
            • • choose odd
                • Manipulate until power 2
        • Different angle
          • • refer identities
        • T Substituition
          • • subs
              • make all T

12. ·

    • use Trigonometric Substitutions
      • • Find x^2, dx
          • subs into eq

13. ·

    • Improper Integral
      • Type I
        • limit have infinity
          • limit approaching
      • Type II
        • limit cause math error
          • limit approaching

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