Basic Analysis I — Real Analysis · Problem 5.5.12

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · improper-integrals

Problem

Suppose f:[1,∞)→Rf : [1, \infty) \to \mathbb{R} is such that g(x)≔x2f(x)g(x) \coloneqq x^2 f(x) is a bounded function. Prove that ∫1∞f\int_1^{\infty} f converges.

Related theory

Browse the problem library