11 Strategies In Integrations

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Mind Map on 11 Strategies In Integrations, created by amyrashazzyra97 on 01/22/2016.
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Mind Map by amyrashazzyra97, updated more than 1 year ago
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Created by amyrashazzyra97 over 8 years ago
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11 Strategies In Integrations
  1. Basic Substitution
    1. 1) Take function that have high power to be as U and differentiate it
      1. 2) Replace integral with variable U and du, the integrate it
        1. 3) After integrate, replace back U with the original function
        2. Completing The Square
          1. Basic substitution is not available
            1. To get 1 constant and 1 variable
            2. Trigonometric Identities
              1. sin2x + cos2x = 1
                1. 1 + tan2x = sec2x
                  1. 1 + cot2x = csc2x
                  2. Addition Formulas
                    1. cos (A+B) = cos A cos B - sin A sin B
                      1. sin (A+B) = sin A cos B + cos A sin B
                      2. Double-Angle Formulas
                        1. sin 2x = 2 sin x cos x
                          1. cos 2x = cos2x - sin2x
                          2. Half-Angle Formulas
                            1. cos2x = (1 + cos2x)/2
                              1. sin2x = (1 - cos2x)/2
                            2. Improper Fraction
                              1. Use long division for polynomials
                                1. Basic substitution is not available
                                2. Separating Fractions
                                  1. Applicable when the fractions can be separated
                                    1. To get simpler integrand
                                    2. Multiplying By A Form of 1
                                      1. Used to multiply the integral by some term divided by itself
                                        1. To get simpler integrand
                                          1. Basic substitution, completing the square, improper fraction, and separating function are not available
                                          2. Eliminating Square Roots
                                            1. Used when have a trigonometric function in the square root
                                              1. Used when trigonometric functions can be simplified by using trigonometric identities to a squared trigonometric form
                                                1. Sketch the graph to solve the absolute integrand
                                                2. Integration By Parts
                                                  1. 1) Integral u dv = uv - integral v du
                                                    1. A right choose of u by using ILATE RULE while dv is easy to integrate
                                                      1. I : INVERSE TRIGO / INVERSE HYPERBOLIC
                                                        1. L : LOGARITHMIC / GENERAL LOGARITHMIC
                                                          1. A : ALGEBRAIC
                                                            1. T: TRIGONOMETRIC / HYPERBOLIC
                                                              1. E : EXPONENTIAL / GENERAL EXPONENTIAL
                                                              2. Used when Basic Substitution, Completing the Square, Trigonometric Identities, Improper Fraction, Separating Fractions, Multiplying by a Form of 1, and Eliminating Square Roots do not work
                                                                1. 2) Tabular Integration ONLY FOR :
                                                                  1. Integral ALGEBRAIC . TRIGONOMETRIC dx
                                                                    1. Integral ALGEBRAIC . EXPONENTIAL dx
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