Minimize integral with variable bounds

1925SpecialistCalculusOptimization

Harvard-MIT Mathematics Tournament

Let $a$ be a positive real number. Find the value of $a$ such that the definite integral $$ \int_{a}^{a^{2}} \frac{\mathrm{d} x}{x+\sqrt{x}} $$ achieves its smallest possible value.

0 students attempted0% solvedRating 1925

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Minimize integral with variable bounds

1925SpecialistCalculusOptimization

Harvard-MIT Mathematics Tournament

Let $a$ be a positive real number. Find the value of $a$ such that the definite integral $$ \int_{a}^{a^{2}} \frac{\mathrm{d} x}{x+\sqrt{x}} $$ achieves its smallest possible value.

0 students attempted0% solvedRating 1925