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32068141
MAPA MENTAL: CÁLCULO DIFERENCIAL E INTEGRAL II
Description
Conceitos básicos do Cálculo Integral para que eles sejam aplicados em diversas áreas do conhecimento que fazem uso desta teoria.
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Jean Lucas
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Created by
Jean Lucas
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MAPA MENTAL: CÁLCULO DIFERENCIAL E INTEGRAL II
INTEGRAL
ANTIDERIVADA
F’(x) = f(x)
INDEFINIDA
∫f(x)dx = F(x)+C ↔ F ’(x) (C)’
PRIMITIVA
INTEGRAÇÃO POR SUBSTITUIÇÃO
u | du
∫ f(g(x)).g’ (x) dx =∫ f(u) du = F(u)+C
INTEGRAÇÃO POR PARTES
∫ u dv = u.v - ∫ v du
u | dv
APROXIMAÇÃO DE ÁREAS
LIMITE
SOMA DE ÁREAS
INTEGRAL DEFINIDA
PROPRIEDADES
∫a b f(x) dx = - ∫b a f(x) dx.
∫a a f(x) dx=0.
∫a b k.f(x) dx = k ∫a b f(x) dx
∫a b [f(x)±g(x)] dx = ∫a b f(x) dx ± ∫a b g(x) dx
∫a b f(x) dx + ∫b c f(x) dx = ∫a c f(x) dx.
∫a b f(x) dx ≤ ∫a b g(x) dx
minf.(b-a)≤∫a b f(x) dx ≤ maxf.(b-a).
f(x) ≥ g(x) em [a,b]→∫a b f(x) dx ≥ ∫a b g(x) dx.
TEOREMA DO VALOR MÉDIO
∫a b f(x) dx = (b-a).f(c).
O TEOREMA FUNDAMENTAL DO CÁLCULO
∫a b f(x) dx = F(b)-F(a)
INTEGRAIS TRIGONOMÉTRICAS
IDENTIDADES TRIGONOMÉTRICAS
REDUÇÃO | RECORRÊNCIA
PRODUTO SENO E COSSENO
SENO E COSSENO DE ARCOS DIFERENTES
PRODUTOS DE TANGENTE E SECANTE
INTEGRAÇÃO POR SUBSTITUIÇÃO TRIGONOMÉTRICA
INTEGRAÇÃO DE FUNÇÕES RACIONAIS POR FRAÇÕES PARCIAIS
INTEGRAIS IMPÓPRIAS
APLICAÇÕES DAS INTEGRAIS DEFINIDAS
AREA ENTRE CURVAS
VOLUME
SÓLIDOS DE REVOLUÇÃO
COMPRIMENTO DE CURVA PLANA
TRABALHO
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