INTEGRATION STRATEGY

ilovemuhammad97
Mind Map by ilovemuhammad97, updated more than 1 year ago
ilovemuhammad97
Created by ilovemuhammad97 about 4 years ago
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Calculas

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INTEGRATION STRATEGY
1 Multiplying by Form of 1
1.1 Plus/Minus at the Denominator (CONJUGATED)
1.2 Simplify expression that can be Integrated
2 Completing the Square
2.1 Quadratic at Denominator (INVERSE TRIGONOMETRIC)
3 Eliminating Square Root
3.1 Trigonometric Identities
3.1.1 Addition Formula
3.1.2 Pythagorean Formula
3.2 Squaring inside --> LOSE SQUARE ROOT
4 Improper Fraction
4.1 Long-Division
4.2
5 Separating Fraction
5.1 Add/Minus at Numerator
6 Partial Fraction Method
6.1 Linear Factor
6.1.1 x have power
6.1.2 Can factorise
6.2 Repeated Linear Factor
6.2.1 Bracket have power
6.3 Irreducible Quadratic Factors
6.3.1 x have power
6.3.2 Cannot Factorise
7 Product
7.1 Integration by Parts
7.1.1
7.1.1.1 u --> easy to Differentiate dv/dx --> easy to Integrate
7.2 Tabular Integration
7.2.1
8 Improper Integral
8.1 Type I
8.2 Type II
9 Trigonometric Identities
9.1 Pythagorean
9.2 Addition
9.3 Double-Angle
9.4 Half-Angle
10 Trigonometric Integrals
10.1 Half-Angle
10.1.1 Power of sin/cos > one
10.2 Reduction Formula
10.2.1
10.2.1.1
10.2.2
10.2.2.1
10.3
10.3.1 ODD Number (Separate)
10.3.2 EVEN Number (Half-Angle Formula)
10.4
10.4.1 Addition Formula
10.5
10.5.1 tan x = t
10.6
10.6.1 tan x/2 = t
11 Trigonometric Substitutions
11.1
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