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Soit \(f:[1,\infty [\rightarrow {\Rr}^{+}\) continue telle que \[\int_{1}^{\infty }f(t)dt\] converge. Montrer que \[\lim\limits_{x\rightarrow \infty }\frac{1}{x}\int_{1}^{x}tf(t)dt=0.\]
Soit \(f:[1,\infty [\rightarrow {\Rr}^{+}\) continue telle que \[\int_{1}^{\infty }f(t)dt\] converge. Montrer que \[\lim\limits_{x\rightarrow \infty }\frac{1}{x}\int_{1}^{x}tf(t)dt=0.\]