TECHNIQUE OF INTEGRATION

TECHNIQUE OF INTEGRATION

1. SQUARE

   • COMPLETING
     • quadratic fuction at denominator
     • no substitution
   • ELIMINATING ROOT
     • trigonometric function in square root
     • form squared trigonomtric

2. TRIGONOMETRIC

   • IDENTITIES
   • INTEGRALS
     • higher power of sin and cos. use reduction formula.
   • SUBSTITUTION
     • variable is replaced by trigo func.

3. FRACTION

   • SEPERATING
     • fraction can be seperated
   • IMPROPER
     • numerator>denominator(long division)

4. RATIONAL FUNCTION

   • numerator<denominator
   • denominator can be factorise
   • when it have quadratic eqn.
     • partial fraction

5. BASIC SUBSTITUTION METHOD

   • simple integral(variable u)

6. MULTPLY (FORM OF 1)

   • term divided by itself

7. IMPROPER INTEGRAL

   • integrate either or both limit infinite
   • the lower and upper limit is infinity
   • it become undefined

8. INTEGRATION BY PART

   • if the 7 other technique cannot be used
   • ILATE
     • u-differentiate
     • dv(u) integrate

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