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
$\frac{10 x}{x+1}=1$ $\Rightarrow x=\frac{1}{9}$
$\frac{10 x}{x+1}=1$ $\Rightarrow x=\frac{1}{9}$
$\frac{10 x}{x+1}=4$ $\Rightarrow x=\frac{2}{3}$
$\frac{10 x}{x+1}=9$ $\Rightarrow x=9$
$\mathrm{I}=9\left(\int_0^{1 / 9} 0 \mathrm{dx}+\int_{1 / 9}^{2 / 3} 1 . \mathrm{dx}+\int_{2 / 3}^9 2 \mathrm{dx}\right)$
$=155$
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