- #1
Pi3.1415
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Hello, I was just wondering if anyone new of a proof that their is no elementary integral for: e^-x^2
Any help would be appreciated.
Any help would be appreciated.
Is there a proof that there is no elementary integral for e^-x^2?
- Thread starter Pi3.1415
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In summary, the conversation is about the possibility of finding an elementary integral for e^-x^2. One person suggests using differential galois theory, but the other person's knowledge on the subject is limited. They mention the existence of Liouville Theorem as a possible solution.
- #2
gb7nash
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Pi3.1415 said:Hello, I was just wondering if anyone new of a proof that their is no elementary integral for: e^-x^2
Any help would be appreciated.
Hi Pi,
If you're interested in proving these, it looks like differential galois theory is your best bet. If you just started taking calculus though, you might have to wait a bit to prove it.
- #3
Pi3.1415
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gb7nash said:Hi Pi,
If you're interested in proving these, it looks like differential galois theory is your best bet. If you just started taking calculus though, you might have to wait a bit to prove it.
Thank you. My knowledge of Galois Theory is weak to put it in a good light, but i don't see how it could be applied in this situation. Could you please help?
- #4
gb7nash
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Pi3.1415 said:
Unfortunately, my knowledge on galois theory is very limited. There might some other simpler method but I don't know it.
- #5
Pi3.1415
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Okay thank you anyway; I *think* I've found a way using Liouville Theorem (which I've never heard of before).
What is the integration of e^-x^2?
The integration of e^-x^2 is a mathematical process used to find the area under the curve of the function e^-x^2. It involves using techniques such as substitution and integration by parts.
Why is the integration of e^-x^2 important?
The integration of e^-x^2 is important because it is used in many fields of science, such as physics, chemistry, and biology. It allows us to solve complex problems and make predictions based on the behavior of the function.
What are the applications of the integration of e^-x^2?
The integration of e^-x^2 has many applications in science and engineering, including calculating probabilities in statistics, solving differential equations in physics, and modeling population growth in biology.
What are some common techniques used to integrate e^-x^2?
Some common techniques used to integrate e^-x^2 include substitution, integration by parts, and partial fractions. These techniques help simplify the function and make it easier to integrate.
Can the integration of e^-x^2 be solved analytically?
No, the integration of e^-x^2 cannot be solved analytically. It is an example of an integral that does not have a closed-form solution and must be solved using numerical techniques or approximations.
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