Can You Solve This Integral?

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In summary, finding an INTEGRAL requires specialized equipment and knowledge in the field of particle physics and is usually discovered through experiments conducted at particle accelerators. The purpose of finding an INTEGRAL is to better understand the fundamental building blocks of the universe and how they interact with each other. Scientists use a variety of techniques to confirm the existence of an INTEGRAL, and while it currently has no practical applications, it may have potential uses in the future as our understanding of it grows.
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Frankww
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I've got a difficult integral, that is, [tex] \int_{-\infty}^{\infty} e^{\lambda x^{2}} dx [/tex]. Could anybody find its solution?
 
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Try http://integrals.wolfram.com/index.jsp"
 
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  • #3
Since, for [itex]\lambda> 0[/itex], that is not bounded as x goes to infinity, and, if [itex]\lambda= 0[/itex], that is just [itex]\int_{-\infty}^{\infty} dx[/itex], neither of those exists.

If, however, [itex]\lambda[/itex] is negative, It is well known that the integral is
[itex]\sqrt{\pi/|\lambda |}[/itex].
 

FAQ: Can You Solve This Integral?

1) Could anybody find an INTEGRAL on their own?

No, finding an INTEGRAL requires specialized equipment and knowledge in the field of particle physics. It is not something that can be done without proper training and resources.

2) How is an INTEGRAL discovered?

An INTEGRAL is usually discovered through experiments conducted at particle accelerators, such as the Large Hadron Collider. Scientists study the results of these experiments to identify new particles, including the INTEGRAL.

3) What is the purpose of finding an INTEGRAL?

The discovery of new particles, like the INTEGRAL, helps scientists better understand the fundamental building blocks of the universe and how they interact with each other. This knowledge can lead to advancements in technology and further our understanding of the universe.

4) How do scientists know they have found an INTEGRAL?

Scientists use a variety of techniques and experiments to confirm the existence of a new particle like the INTEGRAL. This can include analyzing data, conducting simulations, and replicating results in different experiments.

5) Are there any potential applications for the INTEGRAL?

At this time, the INTEGRAL has not been found to have any practical applications. However, as our understanding of this particle and its properties grows, it is possible that it could have potential uses in the future.

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