INTEGRATION STRATEGIES

INTEGRATION STRATEGIES

1. INTERGRATION TABLE

2. SUBSTITUTION METHOD

   • 1. IDENTIFY FUNCTION WITH ITS DIFFERENTIABLE FUNCTION
   • 2. SUBSTITUTE IT INTO "u" AND "du"
   • CONDITION
     • "u" FUNCTION MUST BE POWER

3. COMPLETING THE SQUARE

   • COMPLETE THE SUARE AND INTEGRATE THE FUNCTION
   • CONDITIONS
     • VALID FOR FRACTION ONLY
     • DENOMINATOR HAS QUADRATIC FUNCTION

4. INTEGRATION BY PARTS

   • 1. SUBSTITUTE INTO FORMULA uv-∫v du
   • CONDITION
     • PRODUCT IS NOT DIFFERENTIAL COEFFICIENT OF ANOTHER

5. TRIGONOMETRIC IDENTITIES

   • 1. SIMPLIFY USING TRIGONOMETRIC IDENTITY
   • 2. INTEGRATE

6. TRIGONOMETRIC BY >2

   • 1. USE REDUCTION FORMULA
   • CONDITION
     • USE PRODUCT OF POWER OF SINES AND COSINES METHOD

7. SEPERATING FUNCTION

   • 1. SEPERATE THE FUNCTION
   • 2. USE TRIGONOMETRIC IDENTITY (IF NEEDED)
   • INTEGRATE THE FUNCTION

8. TRIGO INTEGRAL

   • 1. WRITE SUBS FOR X AND CALCULATE DIFFERENTIAL dx
   • 2. SUBTITUTE THE dx
   • 3. INTEGRATE THE FUNCTION
   • 4. REVERSE THE SUBS IN INTEGRATION

9. ELIMINATING THE SQUARE

   • 1. SIMPLIFY USING TRIGO IDENTITIES
   • 2. ELIMINATE THE SQUARE ROOT
   • 3. INTEGRATE

10. IMPROPER INTEGRAL

    • 1. SUBTITUTE a" WITH LIMIT VALUE
    • 2. TAKE LIMIT TO THE INTERGRAL
    • 3. INTEGRATE
    • 4. FIND THE LIMIT SUBS THE VALUE INTO INTEGRATED FUNCTION

11. PARTIAL FRACTION

    • 1. USE LONG DIVISION (IF NUMERATOR>DENOMINATOR)
    • 2. FACTORIZE DENOMINATOR
    • 3. FIND COEFFICIENT

12. MULTIPLY BY FORM OF 1

    • 1. MULTIPLY BY SOME TERM AND DIVIDE BY ITSELF
    • 2. USE TRIGONOMETRIC IDENTITIES
    • 3. INTEGRATE

13. EXPONENTIAL FUNCTION

14. REDUCTION FORMULA

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