- #1
NotEuler
- 55
- 2
I'm pondering something about properties of integrals. What can we say about the following limit?
##\lim_{t\to\infty} \int_t^{\infty } f(x) \, dx##
On one hand, the 'gap' from the lower to upper integration limit diminishes, so that would suggest the limit is always 0.
But what if f is an ever-increasing function? Does the limit exist in that case? Or does the question even make sense, if the integral ##\int_t^{\infty } f(x) \, dx## does not have a finite value?
What would be a formal way to approach a question like this?
##\lim_{t\to\infty} \int_t^{\infty } f(x) \, dx##
On one hand, the 'gap' from the lower to upper integration limit diminishes, so that would suggest the limit is always 0.
But what if f is an ever-increasing function? Does the limit exist in that case? Or does the question even make sense, if the integral ##\int_t^{\infty } f(x) \, dx## does not have a finite value?
What would be a formal way to approach a question like this?