Maxwell-Boltzmann Statistics integral

[Yakadellic]

Hey guys, I have this homework to do, but I can't find a solution.
I need to solve this integral. It's Maxwell-Boltzmann Statistics, we are studying it in class of electronics. So, integral goes like this:
∫from W_s to ∞ [(W-W_s)^(1/2)*e^(W_F-W)/kT]dW

I have looked it up on google, but I couldn't find the solution..
And, W_F,W_s,k and T are constants...
I'll be grateful.

 

[rude man]

You can try wolfram alpha but for the definite integral they'll charge you & the indefinite integral isn't of much help I don't think ...

 

[SteamKing]

Look at this attachment:
http://hep.ph.liv.ac.uk/~hock/Teaching/StatisticalPhysics-Part3-Handout.pdf

Check out Eq. 38 on page 10.

I think with some manipulation, you can get your integral into the form of Eq. 38 which should evaluate to a gamma function of some sort.

 

[Yakadellic]

You can try wolfram alpha but for the definite integral they'll charge you & the indefinite integral isn't of much help I don't think ...

I tried using WolframAlpha, it gives me some result, and it's the right result, but I need the procedure..

Look at this attachment:
http://hep.ph.liv.ac.uk/~hock/Teachi...t3-Handout.pdf

Check out Eq. 38 on page 10.

I think with some manipulation, you can get your integral into the form of Eq. 38 which should evaluate to a gamma function of some sort.

I don't know about that, man.. Professor gave us a "hint", he told us we need to use partial integration method.

 

[Nickie]

I understand your frustration and the importance of finding solutions to problems. The Maxwell-Boltzmann Statistics integral is a fundamental equation used in statistical mechanics to describe the distribution of particles in a gas at a given temperature. It is commonly used in the study of electronics and other fields such as thermodynamics and quantum mechanics.

Unfortunately, there is no single solution to this integral as it depends on the specific values of WF, Ws, k, and T. However, there are various methods and techniques that can be used to approximate or solve this integral, such as numerical integration or using specific mathematical functions.

I recommend consulting with your instructor or classmates for help in solving this integral. Additionally, there are many online resources and textbooks that provide step-by-step solutions to similar integrals. Keep in mind that understanding the concept and theory behind the Maxwell-Boltzmann Statistics integral is just as important as finding the solution.

I wish you the best of luck in your studies and hope you are able to find a satisfactory solution to your homework problem. Remember, as a scientist, perseverance and determination are key qualities in solving complex problems. Keep up the good work!