[Solution] R is the two dimensional region consisting of everything bounded by the lines x+y=0, x-y=0


Question: \(\mathrm{R}\) is the two dimensional region consisting of everything bounded by the lines

\[\begin{aligned} &x+y=0, x-y=0 \\ &x+y=2, x-y=1 \end{aligned}\]

You are given the field Field \([x, y]=\left\{2 x^{2}+y, y^{2}+x^{2}\right\} .\) Calculate the net flow of Field \([x, y\rfloor\) along the boundary of-R by calculating a certain double integral. (Hint: Switch to uv-paper on which you can evaluate this integral as one sweet integral.)

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