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\input 2009-1-C2-prova-VS.dnt

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Cálculo Diferencial e Integral II

PURO-UFF - 2009.1

% Turma: A1/RCT00016

Professor: Eduardo Ochs

{Prova Suplementar (VS) - 13/julho/2009}

}

\bsk
\bsk

1) (2.0 pts) Encontre uma primitiva para $\int \frac{x-1}{x^2 - x -
2} \, dx$.

\msk

2a) (2.0 pts) Calcule $\int \frac {1} {2 + \sqrt[3]{x}} \,dx$. (Obs:
este problema é parecido com o problema 3 da p.524 do Munem).

2b) (1.0 pts) Calcule $\int_{x=8}^{x=27} \frac {1} {2 + \sqrt[3]{x}}
\,dx$.

\msk

3a) (1.2 pts) Calcule $\int x e^{5x}\,dx$.

3b) (0.8 pts) Derive a resposta do item anterior e verifique que ela é
realmente uma primitiva de $x e^{5x}$.

\msk

4) (3.0 pts) (Munem, p.495, problema 11) Calcule $\int \frac {1} {x
\sqrt{1+x^2}} \, dx$.


\bsk
\bsk

Responda de forma legível,

deixe cada passo bem claro,

e verifique suas respostas!

Boa prova!






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