- #1
sapiental
- 110
- 0
I got lost in an example in my book. Hoping someone could explain it to me.For what values of p is the intergral
from 1 to infinity \int \frac {1}{x^p}dx
convergent?
from 1 to infinity \int \frac {1}{x^p}dx
= lim (t -> infinity) \frac {x^-^p^+^1}{-p+1} (from x = 1 to x = t)
= lim (t -> infinity) \frac {1}{p-1} [\frac {1}{t^p^-^1} - 1]
the only thing that confuses me about this is how the t^p-1 ended up in the denominator because after the 2nd sept I get the following:
= lim (t -> infinity) \frac {t^p^-^1}{p-1} - \frac {1}{p-1}
Thanks!
from 1 to infinity \int \frac {1}{x^p}dx
convergent?
from 1 to infinity \int \frac {1}{x^p}dx
= lim (t -> infinity) \frac {x^-^p^+^1}{-p+1} (from x = 1 to x = t)
= lim (t -> infinity) \frac {1}{p-1} [\frac {1}{t^p^-^1} - 1]
the only thing that confuses me about this is how the t^p-1 ended up in the denominator because after the 2nd sept I get the following:
= lim (t -> infinity) \frac {t^p^-^1}{p-1} - \frac {1}{p-1}
Thanks!
Last edited:
