1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Suppose that f is continuous function on the interval [a,b]

  1. Apr 15, 2012 #1
    Suppose that f is continuous function on the interval [a,b]


    integral from b to a If(x)I dx =0 if and only if f(x)=0 for all x in [a,b]

    ıs it true or false ? ı can prove that if f is zero,integral is zero but ı can,'t do that if integral is zero f is zero

    Regards
     
  2. jcsd
  3. Apr 15, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: İntegral

    I assume that your If(x)I is supposed to be |f(x)|.

    If f is not identically 0, there exist some point at which |f(x)| is positive. Since f is continuous, there is some interval on which |f(x)| is postive and so the integral over that interval is positive. And since |f(x)| is never negative there will not be any "canceling".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook