If ∫_0^n[x] dx=66 , then n=

Correct answer: (C) 12. ∫_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)=((n-1) n)/2=66 ⇒ n(n-1)=132 ⇒ n=12

Q73 / 125 · BITSAT 2009 · Mathematics

If \(\int_0^n[x] \mathrm{dx}=66\), then \(n=\)

A
24
B
9
Correct answer
C
12
D
7

Solution

\(\begin{aligned} & \int_0^n[x] d x=\int_0^1 0 d x+\int_1^2 1 d x+\int_2^3 2 d x+\ldots \ldots+ \\ & \int_{n-1}^n(n-1) d x \\ & =1+2+3+\ldots .+(n-1)=\frac{(n-1) n}{2}=66 \\ & \Rightarrow n(n-1)=132 \Rightarrow n=12 \end{aligned}\)

Hence, the correct answer is option: 'C'.

If \(\int_0^n[x] \mathrm{dx}=66\), then \(n=\)

Solution

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