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{\bf HW 6\\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 19}.


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\item Suppose we wish to integrate $f(x,y) = 3x^2-xy+3$ over the rectangle given by $0\leq x\leq 2$, $1\leq y\leq 5$.  Set up this integral using the variable order $dxdy$ but do not compute the answer.

\item Now compute the answer to the previous problem.

\item Repeat problem 1 using variable order $dydx$.

\item Compute the answer to problem 3.

\item Suppose we wish to integrate some function $g(x,y)$ over the triangle with vertices $(0,0)$, $(0,2)$, and $(1,2)$.   Set up this integral using the variable order $dxdy$.  (Do not compute the answer.)

\item Compute the volume of the octahedron in $\mathbb{R}^3$ with vertices at $(0,0, \pm 1), (0,\pm1, 0), (\pm1, 0,0)$. (Hint: exploit the symmetries of the problem to reduce to a problem that may be computed as a simple double integral).

 
 

\end{enumerate}

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