GATE 2025 CS (CS2) – Question 12
The value of $x$ such that $x > 1$, satisfying the equation $\int_1^x t\ln t\,dt = \frac{1}{4}$ is
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Correct answer: (A) $\sqrt{e}$
Explanation
$\int t\ln t\,dt = \frac{t^2}{2}\ln t - \frac{t^2}{4}$. Evaluating from 1 to $x$ and setting it equal to 1/4 gives $x^2(\frac{\ln x}{2} - \frac14) = 0$, so $\ln x = 1/2$ and $x = \sqrt{e}$.