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{\bf HW 8\\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,  November 2}.


\begin{enumerate}

\item Using {\em cylindrical} coordinates, set up the integral to find the volume of the region enclosed by the vertical cylinder $x^2+y^2=4$ and the planes $z=0$ and $y+z=4$.  Do {\bf NOT} evaluate the integral; just set it up.

\item Using {\em spherical} coordinates, set up the integral to find the volume of the region enclosed by the vertical cylinder $x^2+y^2=4$ and the planes $z=0$ and $z=2$.  Do {\bf NOT} evaluate the integral; just set it up.  

\item Consider using the substitution $\begin{cases} x=u-v,\\ y=2u+v\end{cases}$ for the integral of $x+y^2-2$.   What is the {\em integrand} in terms of $u$ and $v$?  (Don't bother with the integral signs, the bounds, or the $du\ dv$.)
  
  
\item Using the same substitution as in the previous problem, suppose the $(x,y)$ region over which we wish to integrate includes the boundary line $2x - y = 3$.  Convert this line into a $(u,v)$ boundary line.





\end{enumerate}

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