# Thread: Integral (continious decreasing functions)

1. ## Integral (continious decreasing functions)

Hi im kinda stuck on this question, any hints are appreciated

I got f:[1,infinity[ -> R, is a positive continious decresing function, and m < n for m,n belonging to N.
I need to show that ∫ from m+1 to n+1 f(x)dx <= sum from k=1 to n of f(k) - sum from k=1 to m of f(k) <= ∫ from m to n f(x)dx

Apologize for the setup, but hopefully its 'readable'

2. Draw it and see the area of the regions.
The widths are one, but since the function is decreasing
the sum is between those two areas.

$\int_{m+1}^{n+1}f(x)dx \le \sum_{k=m+1}^n f(k)\le\int_{m}^{n}f(x)dx$