Q116 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics

If $\int_1^n[x] d x=120$, then $n=$

  • A
    15
  • Correct answer
    B
    16
  • C
    14
  • D
    12

Solution

$\begin{aligned} & \text { } \mathrm{I}=\int_1^n[x] d x=120 \\ & \int_1^2 1 d x+\int_2^3 2 d x+\int_3^4 3 d x+\ldots+\int_{n-1}^n(n-1) d x=120 \\ & \Rightarrow 1+2+\ldots+n-1=120 \Rightarrow \frac{(n-1) n}{2}=120 \\ & \Rightarrow n=16,-15 \text { (rejected) } \Rightarrow n=16\end{aligned}$

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

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