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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^3[x] d x=\ldots$, where $[x]$ is greatest integer function.
  • A
    3
  • B
    0
  • C
    2
  • D
    1
✓

Answer

$\begin{aligned} & \text {(a) : } \int_0^3[x] d x=\int_0^1 0 d x+\int_1^2 1 d x+\int_2^3 2 d x \\ & =\left.x\right|_1 ^2+\left.2 x\right|_2 ^3=(2-1)+2(3-2)=1+2=3\end{aligned}$

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