# Proving integrability of a composition of functions

1. Sep 22, 2011

### bobbyjrock

1. The problem statement, all variables and given/known data
Show that if f is an integrable function on [a,b] then g(x) which is defined to be sin(f(x)) is also integrable

2. Relevant equations

3. The attempt at a solution
I started off by trying to show that since f is integrable it has an Upper sum and a Lower sum where U(f,P)-L(f,P) < $\epsilon$ and then that if you take the sin of Mj and mj that since sin is continuous Mj-mj will also be less than some epsilon. I'm not sure if this works or how to go about it completely. Thanks in advance

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