4353727
Description
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
- Basic Substitution
- 1) Take function that have high power to be as U and differentiate it
- 2) Replace integral with variable U and du, the integrate it
- 3) After integrate, replace back U with the original function
- 1) Take function that have high power to be as U and differentiate it
- Completing The
Square
- Basic substitution is not available
- To get 1 constant and 1 variable
- Basic substitution is not available
- Trigonometric
Identities
- sin2x + cos2x = 1
- 1 + tan2x = sec2x
- 1 + cot2x = csc2x
- 1 + tan2x = sec2x
- Addition Formulas
- cos (A+B) = cos A cos B - sin A sin B
- sin (A+B) = sin A cos B + cos A sin B
- cos (A+B) = cos A cos B - sin A sin B
- Double-Angle Formulas
- sin 2x = 2 sin x cos x
- cos 2x = cos2x - sin2x
- sin 2x = 2 sin x cos x
- Half-Angle Formulas
- cos2x = (1 + cos2x)/2
- sin2x = (1 - cos2x)/2
- cos2x = (1 + cos2x)/2
- sin2x + cos2x = 1
- Improper
Fraction
- Use long division for polynomials
- Basic substitution is not available
- Use long division for polynomials
- Separating
Fractions
- Applicable when the fractions can be
separated
- To get simpler integrand
- Applicable when the fractions can be
separated
- Multiplying By A Form
of 1
- Used to multiply the integral by some term divided by itself
- To get simpler integrand
- Basic substitution, completing the square, improper fraction, and separating function are not available
- Used to multiply the integral by some term divided by itself
- Eliminating Square
Roots
- Used when have a trigonometric function in the square root
- Used when trigonometric functions can be simplified by using
trigonometric identities to a squared trigonometric form
- Sketch the graph to solve the absolute integrand
- Used when have a trigonometric function in the square root
- Integration By
Parts
- 1) Integral u dv = uv - integral v du
- A right choose of u by using ILATE
RULE while dv is easy to integrate
- I : INVERSE TRIGO / INVERSE HYPERBOLIC
- L : LOGARITHMIC / GENERAL LOGARITHMIC
- A : ALGEBRAIC
- T: TRIGONOMETRIC / HYPERBOLIC
- E : EXPONENTIAL / GENERAL EXPONENTIAL
- I : INVERSE TRIGO / INVERSE HYPERBOLIC
- 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
- 2) Tabular Integration ONLY FOR :
- Integral ALGEBRAIC . TRIGONOMETRIC dx
- Integral ALGEBRAIC . EXPONENTIAL dx
- Integral ALGEBRAIC . TRIGONOMETRIC dx
- 1) Integral u dv = uv - integral v du
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