Integrating Strategies Mindmap

Integrating Strategies Mindmap

1. 2.Simplify Integrands

   • Trigonometric Identities
   • Quadratic Expressions
     • Factorise if POSSIBLE
     • Completing the Square (If factorisation doesn't work out)
   • Separating the Fraction
     • Making simple integrands if two expressions share the same denominator
   • Eliminating the Square Root
     • When Trigo function is in the square root
     • When Trigo functions can be simplified to a squared trigo form

2. 3.Look for obvious substitution- "U" substituition

   • Applicable for finding antiderivatives for algebraic and 7 transcendental function
   • Mostly used when expressions are differentiable and being substituted by variables for elimination purposes

3. 4.Identifying the form of integrals

   • Improper Fractions
     • Numerator Power >= Denominator Power
       • Use Long Division Method
   • Either function is not the differential coefficient of the other
     • Use Integration by Parts Method
       • Remember ILATE
   • Antiderivatives for Algebra + Trigo/ Algebra + Expo/ Expo + Trigo
     • Use Tabular Integration Method
   • Rational Functions
     • Partial Fractions
       • Repeated Linear Factor
       • Distinct Linear Factor
         • Use Heaviside "cover up" Method alternatively
       • Irreducible Quadratic Factor
   • Trigo Power >2
     • Use Reduction Formula
     • Use Products of Powers of Sines and Cosines Method
       • CASE 1: m odd
       • CASE 2: m even, n odd
       • CASE 3: both m and n even

4. 1.Always Keep Important Formulas in Mind

Imagens e arquivos do mapa