- #1
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Nevermind sorry, think I've found a sufficent article on wikipedia to help me:
http://en.wikipedia.org/wiki/Gaussian_integral
http://en.wikipedia.org/wiki/Gaussian_integral
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Integrating the Gaussian Integral: Is it as Easy as It Seems?
- Thread starter Zurtex
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In summary, the Gaussian integral is from infinity to negative infinity. If you want something that acts as an anti derivative, try the Error Function (erf(x)). However, this function also has bounds. The problem was in response to a house mate on a physics course who was perplexed about integrating from negative to positive infinity. It was later discovered that he was integrating over the wrong co-ordinates and the integral was much simpler once he transformed it. There was also a similar discussion happening in another thread.
- #2
Gib Z
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From memory the Gaussian integral is from infinity to negative infinity..if you want something that act's as an anti derivative, try the Error Function ( erf(x) )
EDIT: ~sigh~ I just realized the erf(x) also has bounds, my bad.
EDIT: ~sigh~ I just realized the erf(x) also has bounds, my bad.
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Gib Z said:
Thanks, the problem was actually in response to a house mate on a physics course who had this integral and was utterly perplexed how one would integrate it from negative to positive infinity. I remembered it was a standard integral but forgot the details how to do it, anyway in the end it turned out he was integrating over the wrong co-ordinates anyway and it was much more simple once he transformed the integral.
But thanks for trying
- #4
uart
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Zurtex, this was already being discussed in another thread at about the same time as you started this one. See the following link for details :
https://www.physicsforums.com/showthread.php?t=171014
https://www.physicsforums.com/showthread.php?t=171014
- #5
theperthvan
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how about integrating it wrt x. Easy!
1. What is the Gaussian Integral?
The Gaussian Integral, also known as the Normal Integral or the Error Function, is a mathematical function that describes the area under the bell-shaped curve known as the Gaussian distribution. It is used in many fields of science, including statistics, physics, and engineering.
2. How is the Gaussian Integral calculated?
The Gaussian Integral is calculated using the following formula: ∫-∞∞ e-x2 dx. This integral cannot be solved using basic algebraic methods, but can be evaluated numerically or approximated using various techniques, such as the trapezoidal rule or Simpson's rule.
3. What is the significance of the Gaussian Integral?
The Gaussian Integral is significant because it allows for the calculation of probabilities and areas under the Gaussian curve, which is commonly seen in natural phenomena and data sets. It is also used in many mathematical and statistical models, making it a crucial tool in various scientific fields.
4. What are some real-world applications of the Gaussian Integral?
The Gaussian Integral has numerous applications in science and technology. It is used in physics to describe the probability distribution of particles, in engineering to model noise and signal processing, and in statistics to analyze data and make predictions. It is also used in financial modeling, image processing, and many other areas.
5. Are there any limitations to the use of the Gaussian Integral?
While the Gaussian Integral is a powerful tool, it does have some limitations. It assumes that the data follows a normal distribution, which may not always be the case. It also cannot be evaluated using simple algebraic methods, so numerical or approximative techniques must be used. Additionally, it may not provide accurate results for extreme values or outliers in a data set.
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