Solve Integral Function x | Help Appreciated

  • Thread starter Thread starter abia ubong
  • Start date Start date
  • Tags Tags
    Function Integral
AI Thread Summary
The integral of the function x! is not defined in the traditional sense since the factorial function is only applicable to natural numbers. Previous discussions have emphasized the need to consider the gamma function for a broader understanding. The Riemann integral cannot be applied to x! due to its definition limitations. An alternative approach is to use a Stieltjes integral, which involves the step function, allowing the integral from 1 to n to be expressed as a summation of factorials. Understanding these concepts is crucial for properly addressing the integral of x!.
abia ubong
Messages
70
Reaction score
0
hey i need help with this integral ,trhe function is x!,any help will be appreciated
 
Physics news on Phys.org
The factorial is only defined on the natural numbers, as has been made abundantly clear to you in an earlier thread.
Stop posting this nonsense of yours and look up on the gamma function, as you have been advised about earlier.
 
You posted this same question yesterday and have received 16 responses to it. Have you read them? x! is only defined for integers and so does not have a Riemann integral. You could do it as a "Stieljes" integral: \int x! d\alpha(x) where α(x) is the step function. In that case, the integral, from 1 to n, is the sum \Sigma_1^n x!.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Deriving the particle's motion using numerical integration
Replies
5
Views
699
Calculate the area of this pond with functions given for the perimeter
Replies
2
Views
779
Help with this integral on page 34 of Analytical Mechanics by John Bohn
Replies
4
Views
617
Calculating electric charge from graph (capacitor)
Replies
3
Views
1K
Physics Exam Preparation: General question about auxiliary quantity and linearization of a function in physics
Replies
27
Views
1K
Is the line integral of tangential force in pendulum equal to the negative of change in potential energy?
Replies
3
Views
881
How Can Derivatives Determine Speed in Physics Problems?
Replies
20
Views
1K
How to solve this problem in sinusoidal motion? (Satellite orbiting the Earth)
Replies
5
Views
657
Separation of variables: Context of decelerating charged particle
Replies
2
Views
980
Calculus Problem: acceleration, speed, and displacement of a particle
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top