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{\bf HW 7\\Math 261, F18}

Please see the course syllabus for details on how to turn in your homework assignments.  This one is due at the beginning of your class on \underbar{\bf Friday, October 26}.


\begin{enumerate}

\item Set up but do {\bf NOT} evaluate a double integral to compute the integral of $f(x,y) = \cos(xy)$ over the part of the unit disk (the region inside the circle of radius 1 centered at the origin) in the first quadrant (where $x>0$, $y>0$).  
\item Convert the following double integral to an equivalent \underbar{polar} form but do {\bf NOT} evaluate:  $$\displaystyle \int_0^1\int_y^{\sqrt{4-y^2}} x^2+y^2 dxdy$$

\item Set up but do {\bf NOT} evaluate a triple integral to compute the volume of the tetrahedron with vertices $(0,0,0)$, $(1,0,0)$, $(0,2,0)$, and $(0,0,1)$.   The top plane of the tetrahedron is given by $2x+y+2z=2$.   {\bf USE} the order $dz\ dy\ dx$.

\item Consider the tetrahedron $T$ with vertices $(1,0,0)$, $(1, -1, 1)$, $(1,1,1)$, and $(0,0,1)$.  How many regions must $T$ be split into in order to integrate some function over $T$ with the following variable orders (each worth 1 point)?  (Each answer is just 1 number!)
\begin{enumerate}
  \item $dx\ dy\ dz$
  \item $dx\ dz\ dy$
  \item $dy\ dz\ dx$
\end{enumerate}
(It would be good practice to try setting these integrals up, but that's not required for the problem.)

\end{enumerate}

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