JEE Main 2024 — Definite Integration Question with Solution
From: JEE Main 2024 (Online) 30th January Morning Shift
Question
The value of 9 \int_\limits0^9\left[\sqrt{\frac{10 x}{x+1}}\right] \mathrm{d} x, where denotes the greatest integer less than or equal to , is
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Show full solutionCorrect answer: 155
Step-by-step explanation
\begin{aligned} & \mathrm{I}=9\left(\int_\limits0^{1 / 9} 0 \mathrm{dx}+\int_\limits{1 / 9}^{2 / 3} 1\mathrm{d} x+\int_\limits{2 / 3}^9 2 \mathrm{dx}\right) \\ & =155 \end{aligned}
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This is a previous-year question from JEE Main 2024, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.