Q82 / 150 · MHT CET 2021 (24 Sep Shift 2) · Mathematics

$\int_2^5 2[x] d 18x=\{$ where $[x]$ denotes the greatest integer function $\leq x\}$

  • Correct answer
    A
    18
  • B
    16
  • C
    12
  • D
    24

Solution

$\begin{aligned} & \text { Let } I=\int_2^5 2[x] d x \\ & =\int_2^3 2(2) d x+\int_3^4 2(3) d x+\int_4^5 2(4) d x \\ & =4[x]_2^3+6[x]_3^4+8[x]_4^5=4+6+8=18\end{aligned}$

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

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