Solve the Math Puzzle: Help a High School Grad Integrate x!

[abia ubong]

hey i need help with this as a high school grad ,and one people think happens 2 be a maths prodigy a junior student came once and asked me 2 help him integrate x! i could not give a solution ,now pls can anyone help with this puzzle?

 

[matt grime]

What makes you think x! is even a function of a real variable as opposed to one of integers? There is a function Gamma, that agrees with the factorial at the integers, why don't you look it up? The Gamma Function, see, eg, mathworld.

 

[JonF]

Integrating the Gamma function isn’t going to be fun.

 

[matt grime]

And integrating anything is ever fun?

 

[JonF]

The integral of (fu)dn is, such that f and u are constants

 

[matt grime]

Hmm, not my idea of fun, but then all of analysis that isn't trying to be algebra is dull.

 

[Zurtex]

Hmm, not my idea of fun, but then all of analysis that isn't trying to be algebra is dull.

I love analysis, I used to love tricky integrals when I was first learning them as well

Give me any difficult maths challenge and I'll find some fun in it :!)

 

[matt grime]

Evidently you've never sat through a seminar on improving an upper bound from k^2 to k^{1.9999999999} on an eigenvalue of some operator defined on some probably oddly shaped domain, delivered in Russo-English for the benefit of the three other Russian analysts in the room with the poor sodding post grads (who were all algebraists/geometers, if they're different) like me who, at the time, didn't think they should miss these kinds of things.

 

[shmoe]

Even better when you consider the k^2 bound probably takes 15 lines or less to prove while the k^{1.9999999999} takes 15 pages. For 30 pages you can improve this to k^{1.9999999995}.

If something interesting happens at k^{3/2} the next 50 years will see hundreds of impenetrably dense technical pages that improve the bound to k^{1.893453} before someone with a new bright idea comes by and hammers out k^{3/2} on the back of a napkin.

 

[BobG]

The integral of (fu)dn is, such that f and u are constants

Not as fun as $$\frac{dx}{dn}=fu e^{-x}$$ such that f and u are constants. Although it seems more fun while you're doing it than when you're done.

 

[HallsofIvy]

Evidently you've never sat through a seminar on improving an upper bound from k^2 to k^{1.9999999999} on an eigenvalue of some operator defined on some probably oddly shaped domain, delivered in Russo-English for the benefit of the three other Russian analysts in the room with the poor sodding post grads (who were all algebraists/geometers, if they're different) like me who, at the time, didn't think they should miss these kinds of things.

Had a bad semester, Matt?

 

[Zurtex]

Evidently you've never sat through a seminar on improving an upper bound from k^2 to k^{1.9999999999} on an eigenvalue of some operator defined on some probably oddly shaped domain, delivered in Russo-English for the benefit of the three other Russian analysts in the room with the poor sodding post grads (who were all algebraists/geometers, if they're different) like me who, at the time, didn't think they should miss these kinds of things.

Well, I assure you, I may not have had go through something quite so obscure but I've had my pains. I do remember sitting through 7 lectures on Euclid Algorithm, each one explaining no more than the last, in less than 2 weeks because the lecturers never bothered checking with each other what they were covering. I remember sitting through 5 lectures on the Taylor series without ever having ever come to a single example or how you generally derive them, after already previously encountering them thoroughly. The worst one at the moment is my "Advanced" Calculus lecture who knows clearly a lot less about the subject than I do and frequently makes mistakes that are on the level of a P.E high school teacher trying to teach it.

 

[matt grime]

Had a bad semester, Matt?

Oh, not really, I always think that of analysis; do I need a special reason?

 

[abia ubong]

u all not helping i am a high school grad and u all talk of analysis related problems those are not helping ,c'mon u are here 2 help and be helped

 

[Zurtex]

u all not helping i am a high school grad and u all talk of analysis related problems those are not helping ,c'mon u are here 2 help and be helped

f(x)=x! is a function that goes from integers to integers. Generally for something to be integrated it needs to go from real numbers to real numbers, otherwise there is no area underneath it.

 

[abia ubong]

but i have been working on it thugh havenot gotten good result i was tryiong 2 find the general expansio of the factorial mean,but have not gotten it yuet if u can help give a general formula on how 2 expand generally ,i could get it.

 

[matt grime]

For the third time, it makes no sense to talk of integrating x! at the level you're at. It is not a function from the Real line to the Real line. We told you that you need to give a function from R to R, which an be done, (in several, nay, infinitely many ways) that agrees with the factorial at the integers. So, you see, the question does not a priori make sense.