iran-konkur 2015 Q124

iran-konkur · Other · konkur-riazi_1394 Indefinite & Definite Integrals Piecewise/Periodic Function Integration
124- What is the value of $\displaystyle\int_{0}^{2} \left[\frac{x}{2}\right] \frac{\sqrt{x}-1}{x}\, dx$?
  • [(1)] $4 - 2\sqrt{2} - \ln 2$
  • [(2)] $4 - 2\sqrt{2} + \ln 2$
  • [(3)] $2 + \sqrt{2} - \ln 2$
  • [(4)] $2 - \sqrt{2} + \ln 2$
\textbf{124-} What is the value of $\displaystyle\int_{0}^{2} \left[\frac{x}{2}\right] \frac{\sqrt{x}-1}{x}\, dx$?

\begin{itemize}
\item[(1)] $4 - 2\sqrt{2} - \ln 2$
\item[(2)] $4 - 2\sqrt{2} + \ln 2$
\item[(3)] $2 + \sqrt{2} - \ln 2$
\item[(4)] $2 - \sqrt{2} + \ln 2$
\end{itemize}