Questions tagged [approximate-integration]

Use this tag for questions related to approximate integration, which constitutes a broad family of algorithms for calculating the numerical value of a definite integral.

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Approximation of a function using n intervals

Consider the function 𝑓 𝑥 = 𝑠𝑖𝑛 𝑛𝜋𝑥 and divide the domain 0 ≤ 𝑥 ≤ 1 into m intervals. For the “exact” approximation of the function, we will use 𝑚 = 100 intervals. Plot the “exact” function ...
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I have been looking for a numerical quadrature that might be possible to pre-assign specific nodes. For instance, I need to numerically calculate the integral of $f(x)$ in the interval $[a,b]$ but the ...
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I have a set of PDEs governing some function $f(r)$ which I desire to solve via a psuedospectral method (we can consider $f$ to be smooth). It is defined on the interval $r\in[0,\infty)$ with symmetry ...
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The time complexity of integral evaluation

I have the following integral: $$p(x) = \int p(\pmb{\mu})\prod_{i=1}^n\sum_{c_i}p(c_i)p(x_i|c_i,\pmb{\mu})d\pmb{\mu}$$ $\pmb{\mu} \in \mathbf{R}^K$ . The time complexity to numerically evaluate this ...
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Area integral over a function without analytical form

Given a parametric surface $S(u, v): \mathbb{R}^2 \to \mathbb{R}^3$ ($0 \le u,v \le 1$) and an implicit function $f(x,y,z): \mathbb{R}^3 \to \mathbb{R}$, find the integral of $f(\cdot)$ over points on ...
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Integral of the reciprocal of a sum of complex exponentials

I am interested in (realistically, a closed form approximation to) the (real and imaginary parts of the) following integral: $\int_I \frac{1}{\sum_{s=1}^S e^{i a_s x + b_s}} dx$ where $x$ is real and ...
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An integration involving Sinc function

Sir, I have been trying to find out the time average of the Intensity distribution of a scattering problem but I could not find the desired closed form answer of the following integral, which shows ...
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Solution or approximation of $\int_0^r exp(-g*\sqrt{x^2+2*b*x+c})dx$
I'm trying to find a solution or approximation of $$\int_0^r \exp(-g\sqrt{x^2+2bx+c})dx$$ where g > 0, c > 0 and r is from 0 to infinity. I found that $$\frac{1.5}{b*\sqrt{c+1.5}+c+1.5}$$ Works ...