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Romanian District Olympiad 2019 - Grade 12 - Problem 4

Source: Romanian District Olympiad 2019 - Grade 12 - Problem 4

March 16, 2019
Improper integralIntegrallimitcalculus

Problem Statement

Let aa be a real number, a>1.a>1. Find the real numbers b≥1b \ge 1 such that lim⁡x→∞∫0x(1+ta)−bdt=1.\lim_{x \to \infty} \int\limits_0^x (1+t^a)^{-b} \mathrm{d}t=1.
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