The value of the integral $\int_0^{0.9}[x-2[x]] d x$, where [.] denotes the greatest integer function is

The value of the integral $\int_0^{0.9}[x-2[x]] d x$, where [.] denotes the greatest integer function is
  1. $0.9$
  2. $1.8$
  3. $-0.9$
  4. 0

Solution

Since $\int_0^a[x]=0$ where $0 \leq a \leq 1$ $ \therefore \int_0^{0.9}[x-2[x]] d x=0 $

Asked in: JEE Main 2012 (19 May Online)

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