Q100 / 150 · MHT CET 2022 (10 Aug Shift 2) · Mathematics

$\int_0^2|2 x| \mathrm{d}=$ (where [.] denotes the greatest integer function.)

  • A
    4
  • Correct answer
    B
    3
  • C
    2
  • D
    5

Solution

$\begin{aligned} & \int_0^2[2 x] \mathrm{d} x=\int_0^{1 / 2} 0 \mathrm{~d} x+\int_{\frac{1}{2}}^1 1 \cdot \mathrm{d} x+\int_1^{3 / 2} 2 \mathrm{~d} x+\int_{\frac{3}{2}}^2 3 \mathrm{~d} x \\ & =0+\left(1-\frac{1}{2}\right)+2\left(\frac{3}{2}-1\right)+3\left(2-\frac{3}{2}\right) \\ & =0+\frac{1}{2}+2 \times \frac{1}{2}+3 \times \frac{1}{2}=3\end{aligned}$

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

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