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\begin{document}

\begin{center}
  \Large{12. Gyak.}
  
  \small{térfogati integrálok, integrál transzformáció
  
  ($\operatorname{d}V\equiv\operatorname{d}(x, y, z)$)}
  \end{center}

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\begin{enumerate}
 \item 
  \[\iiint_{M} (1-x-z)\operatorname{d}V=?\]
  \[ M= \left\{ (x,y, z)\in \mathbb{R}^3 | 0\leq x\leq 1, 0\leq y \leq 1, 0\leq z\leq x^2+y^2+2\right\}\]
  
 \item 
   \[
     \int_{0}^1 \int _{0}^{1-x} \int_{0}^{1-x-y} \frac{1}{(1+x+y+z)^3} \operatorname{d}V=?
   \]
   (Mi a tartomány?)
 \item 
   \begin{align*}
     & \iiint_{V} x^2 y z \operatorname{d}x\operatorname{d}y\operatorname{d}z=? && V: x^2+y^2+z^2\leq 1, x\leq 0, y\leq 0, z\leq 0
   \end{align*}
 
 \item 
  \[\iiint_{M} (\sqrt{y^2+z^2}+x)\operatorname{d}V=?\]
  \[ M= \left\{ (x,y, z)\in \mathbb{R}^3 | 0\leq x\leq 2, y^2+z^2\leq 1 \right\}\]
  
 \item 
   \[\iiint_{M} (\sin \sqrt{x^2+y^2}+2z)\operatorname{d}V=?\]
  
 \hspace{0.5cm}
  
 \begin{tabular}{ccc}
    \includegraphics[scale=0.4]{12_1.pdf} & \includegraphics[scale=0.5]{12_4.pdf} & \includegraphics[scale=0.5]{12_5.pdf} \\
	1. feladat & 4. feladat & 5. feladat
 
 \end{tabular}
 \end{enumerate}

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