JEE Mains · Maths · STD 12 - 7.2 definite integral
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 ...........
- A \(155\)
- B \(166\)
- C \(444\)
- D \(421\)
Answer & Solution
Correct Answer
(A) \(155\)
Step-by-step Solution
Detailed explanation
\(\frac{10 x}{x+1}=1\) \(\Rightarrow x=\frac{1}{9}\) \(\frac{10 x}{x+1}=4\) \(\Rightarrow x=\frac{2}{3}\) \(\frac{10 x}{x+1}=9\) \(\Rightarrow x=9\) \(\mathrm{I}=9\left(\int_0^{1 / 9} 0 \mathrm{dx}+\int_{1 / 9}^{2 / 3} 1 . \mathrm{dx}+\int_{2 / 3}^9 2 \mathrm{dx}\right)\)…
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