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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
The value $9 \int_0^9\left[\sqrt{\frac{10 x}{x+1}}\right] d x$, where $[t]$ denotes the greatest integer less than or equal to $t$, is___________.
  • ✓
    $155$
  • B
    $166$
  • C
    $444$
  • D
    $421$
✓

Answer

Correct option: A.
$155$
a
$\frac{10 x}{x+1}=1$           $\Rightarrow x=\frac{1}{9}$

$\frac{10 x}{x+1}=4$           $\Rightarrow x=\frac{2}{3}$

$\frac{10 x}{x+1}=9$           $\Rightarrow x=9$

$\mathrm{I}=9\left(\int_0^{1 / 9} 0 \mathrm{dx}+\int_{1 / 9}^{2 / 3} 1 . \mathrm{dx}+\int_{2 / 3}^9 2 \mathrm{dx}\right)$

$=155$

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