Integral limit equals one find b

2300ExpertCalculus

2019 ROMANIAN MATHEMATICAL OLYMPIAD · 2019

Given a real number $a > 1$, determine all real numbers $b \ge 1$ such that $$ \lim_{x \to \infty} \int_{0}^{x} (1 + t^a)^{-b} \, dt = 1. $$

0 students attempted0% solvedRating 2300

Related practice paths

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.

2300ExpertCalculus

2019 ROMANIAN MATHEMATICAL OLYMPIAD · 2019

Given a real number $a > 1$, determine all real numbers $b \ge 1$ such that $$ \lim_{x \to \infty} \int_{0}^{x} (1 + t^a)^{-b} \, dt = 1. $$

0 students attempted0% solvedRating 2300