Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have this question which asks for a 2*pi periodic function on the reals, that is integrable on [-pi, pi] but fails to satisfy the mean value theorem for integrals.

The question also says to help answer the above question, you may wish to show that the function:

g: [0,1] -> reals given by,

g(x) = sin(1/x) if x is non-zero

g(x) = 0 if x=0

Now I've shown that the above function is true, but I have no idea how to show that it fails to satisfy the mean value theorem or how it relates to a function that is 2*pi periodic and integrable on the given interval.

Please help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mean value theorem for integrals

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**