QJEEM24Ma4eb1: JEE Main 2024 Mathematics - Class 12 JEEM24Ma4eb1 Solution: The value of 9 ∫ 0 9 [ 10 x x + 1 ] d x , where [ t ] denotes…

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QJEEM24Ma4eb1: JEE Main 2024 Mathematics - Class 12 JEEM24Ma4eb1 Solution: The value of 9 ∫ 0 9 [ 10 x x + 1 ] d x , where [ t ] denotes…

The value of $9 \int_{0}^{9} [\sqrt{\frac{10 x}{x + 1}}] d x$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is

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$\begin{array}{ll} \frac{10 x}{x + 1} = 1 & \Rightarrow x = \frac{1}{9} \\ \frac{10 x}{x + 1} = 4 & \Rightarrow x = \frac{2}{3} \\ \frac{10 x}{x + 1} = 9 & \Rightarrow x = 9 \end{array}$

$\begin{aligned} I = 9 (\int_{0}^{1 / 9} 0 dx + \int_{1 / 9}^{2 / 3} 1 d x + \int_{2 / 3}^{9} 2 dx) \\ = 155 \end{aligned}$

QJEEM24Ma4eb1: JEE Main 2024 Mathematics - Class 12 JEEM24Ma4eb1 Solution: The value of 9 ∫ 0 9 [ 10 x x + 1 ] d x , where [ t ] denotes…

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