solução da E. D. : dp/dt = kL²ln t , L(1) = -1

Cálculo II

•

UNISAL

0

Samia Francisco

01/05/2018

Você sabe responder essa pergunta?

Crie uma conta e ajude outras pessoas compartilhando seu conhecimento!

RD Resoluções

02.06.2018

Aplicando a integral para resolver o P. V. I, temos:

$\displaystyle\int \frac{x}{( x^{2} +9)^{ \frac{1}{2} } } \\\\\\\
Fazendo~~por ~~substituic\~ao!\\\\\\\\
u= x^{2} +9\\\\\
du=2xdx\\\\\\
 \boxed{\frac{du}{2}=xdx}$

$\displaystyle\int \frac{1}{2 \sqrt{u} } } \\\\\\\

 \dfrac{1}{2} \displaystyle\int \frac{1}{\sqrt{u} } } \\\\\\\
\dfrac{1}{2} \displaystyle\int \frac{1}{\sqrt{x} } } \\\\\\\

\dfrac{1}{2} \displaystyle\int \frac{1}{(x)^{ \frac{1}{2} } } } \\\\\\\

\dfrac{1}{2} \displaystyle\int (x)^{ -\frac{1}{2} } } } \\\\\\\

\dfrac{1}{2} \displaystyle\int \frac{ (x)^{ -\frac{1}{2}+1 } }{- \frac{1}{2} +1} } } \\\\\\\

\dfrac{1}{2} \displaystyle\int \frac{ (x)^{\frac{1}{2} } }{ \frac{1}{2}}





$

Poranto, teremos:

$\displaystyl (x)^{\frac{1}{2}}\\\\\\
x=u\\\\\\



 \displaystyle\int \frac{x}{( x^{2} +9)^{ \frac{1}{2} } }=\sqrt{ x^{2} +9}+c 


$