# Tagged Questions

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Newton-Cotes quadrature formulas are a generalization of trapezoidal and Simpson's rule. The trapezoidal rule involves $2$ points, Simpson's rule involves $3$, and in general Newton-Cotes formulas ...
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I noticed that all quadrature methods I know (Newton-Cotes and Gaussian quadrature) have always even order in the sense that a quadrature method is of order $n$, if all polynomials of degree $n-1$ are ...
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### Order of Romberg's method

We call a method(numerical integration) of $n-$th order, if it can integrate any polynomial of degree $n-1$ without any error. In this sense: The simpson rule is of $4$-th order and the trapezium ...
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### Compute $\int_{A}^{B}\prod_i \frac{(x-A_i)^{\alpha_i-1}(B_i-x)^{\beta_i-1}}{(B_i-A_i)^{\alpha_i+\beta_i-1}\mathrm{B}(\alpha_i,\beta_i)}\mathrm{d}x$

I need a fast and accurate method to evaluate numerically the following integral: ...
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### Numerical integration fails

I am doing something wrong. This is my algorithm to evaluate the integral $$\int_0^1 \frac{1}{1+x}dx= \log(2).$$ with the Newton Cotes algorithm (Simpson and 3/8). Both give me that for large n ...
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### How to evaluate $I=\iiint dr_{12}dr_{13}dr_{14}$ analytically/numerically?

How to evaluate this integral analytically or numerically: $$I=\iiint dr_{12}dr_{13}dr_{14}$$ constrained by $$r_{12}<r_0,\\r_{23}<r_0,\\r_{34}<r_0,$$ where $r_0$ is a given real ...
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### Numerical integration given a derivative of a function of two dependent variables

I want to solve the following equation of an integral valued function: $Q = \int_{0}^{x_p}f(t_p,x)dx$ for some particular $x_p$ at a fixed time $t_p$, given some known $Q$ and an initial $f(0,x)$. ...