1. The problem statement, all variables and given/known data f(x) is a bounded function and integrable on [a,b] . a, b are real constants. We have to prove that i) An = a∫b f(x)cos(nx) dx → 0 when n→∞ ii)Bn = a∫b f(x)sin(nx) dx → 0 when n→∞ 2. Relevant equations Parseval's formula : For uniform convergence of f(x) with its fourier series in [a,b] a∫bf2(x) dx = L * ( a02/2 + Ʃ( an2+bn2 ) ) where a0 an bn are Fourier Coefficient. L = (b-a)/2 3. The attempt at a solution If f(x) is bounded integrable in [-π,π] Then by Parseval's Theorem -π∫πf2(x) dx = L * ( A02/2 + Ʃ( An2+Bn2 ) ) Hence Ʃ( An2+Bn2 ) ) ≤ 1/L * ( -π∫πf2(x) dx ) Hence Ʃ( An2+Bn2 ) ) converges to a finite value. Hence An → 0 when n→∞ and Bn → 0 when n→∞ The above proof is assumed the interval is [-π,π] . But the problem is when interval is [a,b]. Fourier coefficient An is given by (1/L)*a∫b f(x)cos(nπx/L) dx Any idea How to proceed further?