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O gráfico de \(g\) em \([0,4]\) é dado abaixo
Seja \[ A(x) = \int _0^x g(t) \d t \] para \(0\leq x\leq 4\).
Então sabemos que \(A(2)\) é positivonegativozero. Além disso, \(A(3.8)\) é positivonegativozero e \(A'(3.8)\) é positivonegativozero.
xmhintLembre-se: \(A(2)=\int _0^2 g(t) \d t\). Isso dá a área
com sinal.
xmhintLembre-se: \(A(3.8)=\int _0^{3.8} g(t) \d t\). Isso dá a área com sinal.
\(A(3.8)=\int _0^{3.8} g(t) \d t=\int _0^2 g(t) \d t+\int _2^{3.8} g(t) \d t\).
A primeira integral é negativa e a segunda, positiva.
xmhintLembre-se: \(A'(x)=g(x)\)
xmhintLembre-se:
\(A'(3.8)=g(3.8)>0\)
Determine a solução do problema de valor inicial \(y'(x) = g(x)\) e \(y(0) = 2\).
\(y(x)=g(x)\) \(y(x)=g(x)+2\) \(y(x)=A(x)\) \(y(x)=A(x)+2\) \(y(x)=g'(x)\) \(y(x)=g'(x)+2\) Nenhuma
das anteriores
Determine uma expressão para \(\int _0^4 \left |g(t)\right | \d t\).
\(A(4)\) \(A(2)-A(4)\) \(A(4)-A(2)\) \(A(4)-2A(2)\) Nenhuma das anteriores
Determine a soma de Riemann do ponto médio para \(g\) em \([0,4]\) com 2 subintervalos.
\(g(1)+g(3)\) \(g(0)+g(2)\) \(g(2)+g(4)\) \(2g(1)+2g(3)\) \(2g(0)+2g(2)\) \(2g(2)+2g(4)\) Nenhuma das anteriores
![[Picture]](/rendered/firstFundamentalTheoremOfCalculus/exercises/FFTOC5-52a62be10682c498845aa45732df8958.svg)