Let f(x) be a continuous functions on [0,∞) and that ∫ |f(t)|^2dt is convergent for 0≤t<∞.(adsbygoogle = window.adsbygoogle || []).push({});

Let ∫ |f(t)|^2dt for 0≤t<∞ equals F.

Show that lim(σ→∞) ∫(1-x/σ)|f(x)|^2 dx for0≤x≤σ converges to F.

I know that it needs to prove that lim(σ→∞) ∫(x/σ)|f(x)|^2 dx for0≤x≤σ converges to 0. Can anyone give me a hint??

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# Convergence of an Improper Integral

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