H = [a,b][tex]\times[/tex][c,d] . f[tex]\rightarrow[/tex]R is continuous, and(adsbygoogle = window.adsbygoogle || []).push({});

g:[a,b][tex]\rightarrow[/tex]R is integrable.

Prove that

F(y) = [tex]\int[/tex]g(x)f(x,y)dx from a to b is uniformly continuous.

I initially ripped g(x) and f(x,y) apart and tried to show each was continuous. This failed.

In short, I am completely stuck. Please help me.

**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!

# Homework Help: Show integrable is uniformly continuous

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