If ∫ 0 n [ x ] dx = 66 , then n =

∫ 0 n [ x ] d x = ∫ 0 1 0 d x + ∫ 1 2 1 d x + ∫ 2 3 2 d x + …… + ∫ n − 1 n ( n − 1 ) d x = 1 + 2 + 3 + … . + ( n − 1 ) = 2 ( n − 1 ) n = 66 ⇒ n ( n − 1 ) = 132 ⇒ n = 12

Mathematics - Pair of Lines Question with Solution | TestHub

MathematicsPair of LinesGeneralMedium2 minPYQ_2009

MathematicsMediumsingle choice

If $\int_{0}^{n} [x] dx = 66$ , then $n =$

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Solution:

$\int_{0}^{n} [x] d x = \int_{0}^{1} 0 d x + \int_{1}^{2} 1 d x + \int_{2}^{3} 2 d x + \dots\dots + \int_{n - 1}^{n} (n - 1) d x = 1 + 2 + 3 + \dots . + (n - 1) = \frac{( n - 1 ) n}{2} = 66 \Rightarrow n (n - 1) = 132 \Rightarrow n = 12$

Stream:BITSATSubject:MathematicsTopic:Pair of LinesSubtopic:General

⏱ 2mℹ️ Source: PYQ_2009

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