Let f be a Lebesgue integrable function in the interval [a,b]
lim integral from a to b (f(x)*|cosnx|) = 2/pi * integral from a to b (f(x))
Every measurable function can be approximated arbitrarily close by simple functions.
The Attempt at a Solution
I've solved part i of the problem (which was to show the same setup except f*cosnx instead of f*|cosnx|) has an integral equal to zero.
I'm pretty stuck on this part - I'm sure I have to find a simple function but I'm not sure what a good simple function would be.