Integration

# Integration - Vineet Goyal Differentials Indefinite...

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QSRP - Chapter 14 1 Vineet Goyal Differentials Indefinite Integrals Initial Conditions Integration Formulas Integration techniques Summation Definite integral Fundamental theorem Area Area between curves Surplus Quantitative Skills Review Program Integration Chapter 14

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QSRP - Chapter 14 2 Vineet Goyal Differentials Indefinite Integrals Initial Conditions Integration Formulas Integration techniques Summation Definite integral Fundamental theorem Area Area between curves Surplus Differentials Definition (dy/dx = f n (x)) dy = f n (x) Δx Use: Δy ≈ dy Examples - Page 620 of text
QSRP - Chapter 14 3 Vineet Goyal Differentials Indefinite Integrals Initial Conditions Integration Formulas Integration techniques Summation Definite integral Fundamental theorem Area Area between curves Surplus Indefinite Integral Anti-derivative of f(x) is F(x) such that F'(x) = f(x) dF(x) = f(x) dx Indefinite integral ∫f(x) dx = F(x) + C Technique 1: Guess the anti-derivative Integral sign Integrand Constant of integration x is the variable on integration

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QSRP - Chapter 14 4 Vineet Goyal Differentials Indefinite Integrals Initial Conditions Integration Formulas Integration techniques Summation Definite integral Fundamental theorem Area Area between curves Surplus Indefinite Integral Basic integration formulas Page 625 of text Examples from notes
QSRP - Chapter 14 5 Vineet Goyal Differentials Indefinite Integrals Initial Conditions Integration Formulas Integration techniques Summation Definite integral Fundamental theorem Area Area between curves Surplus Integrations with initial conditions y = ∫f(x) dx = F(x) + C If I know y(x 0 ) = y 0 , I can find C C = y 0 – F(x 0 ) Example from notes

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Integration - Vineet Goyal Differentials Indefinite...

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