Let a,b be real numbers such that 0 < a < b < infinity. Does the limit
lim of ( integral from a to b of n*sin (x^2/n) dx , n is positive integer
exist? ( prove or disprove). Find the limit if it exists. Prove all assertions and justify every step.
The integral here is with respect of Lebesgue measure.
Lebesgue Measures, Limits and Integrals are investigated. The solution is detailed and well presented.