Chris
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How do I find the area of this domain given $ D = \{(x,y) | x^2 \le y, x+y \le 6, y - 2x \le 3?$
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Noting that the intersection points are at $(1,5)$, $(2,4)$ and $(-1,1)$, the area is $$ \int_{-1}^{1}(2x+3)dx+\int_{1}^{2}(6-x)dx-\int_{-1}^{2}x^{2}dx=\frac{15}{2} $$

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Leading order behaviour of an infinite sum
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1 votes

I've managed to work out the answer using the stationary phase method and I've checked it numerically in Mathematica. For interest, it is $$ \sum_{m=-\infty}^{\infty}\frac{e^{i\left(\alpha m+k\sqrt{R^{...

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Divergence on a parameterised surface
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0 votes

I've worked out the answer. For interest it is $$ \nabla\cdot\textbf{A}=\partial_{s}A_{s}+\partial_{t}A_{t}+\frac{\partial_{s}|\partial_{s}\textbf{r}\times\partial_{t}\textbf{r}|}{|\partial_{s}\...

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Leading order behaviour of a doubly infinite sum
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0 votes

I've managed to work out the answer using the stationary phase method and I've checked it numerically in Mathematica. For interest, it is $$ \sum_{m,n=-\infty}^{\infty}\frac{e^{i(\alpha m+\beta n+\...

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