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Question: Answered & Verified by Expert
The value of the integral $\int_0^{0.9}[x-2[x]] d x$, where [.] denotes the greatest integer function is
MathematicsDefinite IntegrationJEE MainJEE Main 2012 (19 May Online)
Options:
  • A
    $0.9$
  • B
    $1.8$
  • C
    $-0.9$
  • D
    0
Solution:
2126 Upvotes Verified Answer
The correct answer is:
0
Since $\int_0^a[x]=0$ where $0 \leq a \leq 1$
$$
\therefore \int_0^{0.9}[x-2[x]] d x=0
$$

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