How does the probability density function handle infinity in integrals?

[converting1]

http://gyazo.com/02812d5d8f1d07c72153c9f66740e147

I've dealt with integrals with infinity before. When considering the part x >= 1 , do I take the limit as if it's a very large number? i.e. $\int_0^{\infty} x^{-2.5} \ dx = 2/3$ ?

 

[UltrafastPED]

Yes, take the limit as the upper value goes to infinity.

 

[LCKurtz]

http://gyazo.com/02812d5d8f1d07c72153c9f66740e147

I've dealt with integrals with infinity before. When considering the part x >= 1 , do I take the limit as if it's a very large number? i.e. $\int_0^{\infty} x^{-2.5} \ dx = 2/3$ ?

You mean $\int_1^\infty$. What you have written would diverge.

 

[converting1]

ok thank you