Solving the Strange Integral - x! to x!∞

In summary: However, if you are talking about integers, then yes, the last one (i.e. the largest one) will always be odd.In summary, the conversation discusses the misconception of the integral of x! and the truth about it being the Gamma function. It also touches on the concept of there being a "last number" and whether it will be odd or even. Ultimately, while there is no last real number, the last integer will always be odd.
  • #1
abia ubong
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0
Hi, i was working with my teacher, and i discovered the continuous differential of x!gives x!,also the continuous integral to infinity of x! gives x!.how true is this ,also i wanted to know if the last number ever is going to be odd or even ,because from my point of view the ranges of all numbers is between 0-9since 0 is even and 9,the last is odd,then the last number in this world should be odd. Pls do not ignore this like you always do i need this urgently.
Thanks
 
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  • #2
There's no such thing as the integral of [itex] x! [/itex].However,Gamma-Euler can be integrated under certain conditions on domains from [itex] \mathbb{C} [/itex].

Daniel.
 
  • #3
abia ubong said:
Hi, i was working with my teacher, and i discovered the continuous differential of x!gives x!,also the continuous integral to infinity of x! gives x!.how true is this ,

Why are people trying to differentiate or integrate x! lately? Even if I give you the benefit of the doubt and assume you're talking about the usual extension of x! to the reals, namely the Gamma function, what you've written looks like nonsense. Gamma is not it's own derivative.

abia ubong said:
..also i wanted to know if the last number ever is going to be odd or even ,because from my point of view the ranges of all numbers is between 0-9since 0 is even and 9,the last is odd,then the last number in this world should be odd.

There is no "last number". Given any real number x, there is a larger one x+1, so how can there be a "last" one?
 

FAQ: Solving the Strange Integral - x! to x!∞

What is the concept of solving the strange integral - x! to x!∞?

The strange integral - x! to x!∞ is a mathematical problem involving the integration of the factorial function, which is represented by the symbol "!" and is used to calculate the products of consecutive integers. The "x! to x!∞" part indicates that the integral is evaluated from the factorial of x to infinity.

Why is solving this integral considered strange?

The strangeness of this integral comes from the fact that the factorial function is a discrete function, meaning it only takes integer values, while integration is typically performed on continuous functions. This makes the process of solving the integral more complex and challenging.

What are the possible methods for solving this integral?

There are several approaches that can be used to solve this integral, including using the properties of the factorial function, applying integration techniques such as substitution or integration by parts, or utilizing specialized mathematical software.

What are the applications of solving this integral?

Solving this integral can be useful in various fields of mathematics and science, such as statistics, probability, and physics. It can also be used to solve other types of integrals involving discrete functions.

Is there a general formula for solving the strange integral - x! to x!∞?

No, there is no general formula for solving this integral as the approach may vary depending on the specific function being integrated. However, there are certain techniques and properties that can be applied to simplify the process of solving it.

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