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### 2d quadrature weights for an arbitrary set of nodes

I need to estimate the value of a 2d integral
$\int_{y_{min}}^{y_{max}}dy \int_{x_{min}}^{x_{max}} dx \, f(x,y) P(x,y)$
I have the an explicit analytical form for $P(x,y)$.
I have samples of the ...

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### Area Under Generalized Parabolas and Hyperbolas without Calculus

This is shorter and more specific version of certain questions about a rather simple quadrature method. The answers I got were great but not what I asked. The terms in the title for $y=x^p$ look ...