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### Integrating Powers without much Calculus

I'll jump into the question and then back off into qualifications and context
Using the definition of a definite integral as the limit of Riemann sums, what is the best way (or the very good ways) ...

**6**

votes

**1**answer

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### Approximation of an integral of a concave function

I suspect this is a homework question somewhere, but I've not seen it elsewhere and it seems like it should be easy: let $f(x)$ be a concave function from $[0,1]$ to the reals such that $f(0) = f(1) ...

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**0**answers

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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 ...

**1**

vote

**1**answer

296 views

### gaussian quadrature

Gaussian quadrature allows us to integrate polynomials up to order $2 n-1$ using only $n$ function values.
$\int_{x_0}^{x_1} ( \sum_{i=0}^{2 n-1} a_i x^i ) dx = f(a_0, \dots , a_{2 n-1}) $
thus, the ...

**1**

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**0**answers

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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 ...