4335568
Description
Mind Map by Amalia Azlizuddi, updated more than 1 year ago
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Created by Amalia Azlizuddi
over 8 years ago
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Integration Strategy
- Basic Substitution Method
- Trigonometric Functions
- ᶴ sin x dx = - cos x + C
Annotations:
- ᶴ sin x dx= - cos x + C ᶴ cos x dx = sin x + C ᶴ sec2 x dx = tan x + C ᶴ sec x tan x = sec x + C ᶴ csc2 x dx = - cot x + C ᶴ csc x cot x dx = - csc x + C
- ᶴ cos x dx = sin x + C
- ᶴ sec^2 x dx = tan x + C
- ᶴ sec x tan x = sec x + C
- ᶴ csc^2 x dx = - cot x + C
- ᶴ csc x cot x dx = - csc x + C
- ᶴ csc x cot x dx = - csc x + C
- ᶴ csc^2 x dx = - cot x + C
- ᶴ sec x tan x = sec x + C
- ᶴ sec^2 x dx = tan x + C
- Trigonometric
Identities
- cos^2 Ө + sin^2 Ө = 1
- 1 + tan^2 Ө = sec^2 Ө
- 1 + cot^2 Ө = csc^2 Ө
- 1 + cot^2 Ө = csc^2 Ө
- 1 + tan^2 Ө = sec^2 Ө
- cos^2 Ө + sin^2 Ө = 1
- Addition Formula
- cos (A + B) = cos A cos B – sin A cos B
- sin (A + B) = sin A cos B + cos A sin B
- cos (A + B) = cos A cos B – sin A cos B
- Double Angle Formula
- cos 2Ө = cos^2 Ө - sin^2 Ө
- sin 2Ө = 2 sin Ө cos Ө
- sin 2Ө = 2 sin Ө cos Ө
- cos 2Ө = cos^2 Ө - sin^2 Ө
- Half-Angle Formula
- ᶴ sin x dx = - cos x + C
- Natural Logarithm
- ∫ 1/u du = ln |u| + C
- ∫ 1/u du = ln |u| + C
- Exponential Functions
- ∫ e^u du = e^u + C
- ∫ e^u du = e^u + C
- General Exponential Functions
- ∫ a^u du = a^u/ln a + C
- ∫ a^u du = a^u/ln a + C
- Inverse Trigonometric Functions
- Hyperbolic Functions
- ∫ sinh u du = cosh u + C
- ∫ cosh u du = sinh u + C
- ∫ sech^2 u du = tanh u + C
- ∫ csch^2 u du = - coth u + C
- ∫ sech u tanh u du = - sech u + C
- ∫ csch u coth u du = - csch u + C
- ∫ csch u coth u du = - csch u + C
- ∫ sech u tanh u du = - sech u + C
- ∫ csch^2 u du = - coth u + C
- ∫ sech^2 u du = tanh u + C
- ∫ cosh u du = sinh u + C
- ∫ sinh u du = cosh u + C
- Inverse Hyperbolic Functions
- Trigonometric Functions
- Completing the Square
- ax^2 + bx + c = 0
- x^2 + b/a x + c/a = 0
- x^2 + b/a x + c/a = 0
- ax^2 + bx + c = 0
- Trigonometric Identities
- - summation of two terms
power two
- - Different angle
- ᶴ csc x dx = -ln l csc x + cot x l + C
- ᶴ sec x dx = ln l sec x + tan x l + C
- ᶴ tan x dx = -ln l cos x l + C
- ᶴ cot x dx = ln l sin x l + C
- ᶴ cot x dx = ln l sin x l + C
- ᶴ tan x dx = -ln l cos x l + C
- ᶴ sec x dx = ln l sec x + tan x l + C
- ᶴ csc x dx = -ln l csc x + cot x l + C
- - Different angle
- - summation of two terms
power two
- Improper Fraction
- ᶴ polynomial/polynomial
- (Degree of numerator ≥ Degree of
denominator)
- Long Division Method
- Long Division Method
- (Degree of numerator ≥ Degree of
denominator)
- ᶴ polynomial/polynomial
- Separating Functions
- (a + b)/c = a/c + b/c
- (a + b)/c = a/c + b/c
- Multiplying by a Form of 1
- Eliminating Square Roots
- Trigonometric Functions win the Square Root
- the Trigonometric Functions can be Simplified to Eliminate the Square Roots
- Trigonometric Functions win the Square Root
- Integration by Parts
- Either function is not the differential coefficient of the other
- eg:: ᶴ x^2 ln x dx
- ᶴ u dv = uv – ᶴ v du
- ᶴ u dv = uv – ᶴ v du
- eg:: ᶴ x^2 ln x dx
- Either function is not the differential coefficient of the other
- Trigonometric Integrals
- ᶴ sin2 x dx = ½ ᶴ ( 1 – cos 2x) = x/2 – sin2x/4 + C
- ᶴ cos2 x dx = ½ ᶴ ( 1 + cos 2x) = x/2 + sin2x/4 + C
- ᶴ cos2 x dx = ½ ᶴ ( 1 + cos 2x) = x/2 + sin2x/4 + C
- ᶴ sin2 x dx = ½ ᶴ ( 1 – cos 2x) = x/2 – sin2x/4 + C
- Trigonometric Substitutions
- Improper Intergral
- Type 1
- Type 2
- Type 1
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