The value of the integral _0^ 0.9 [ - 2[x]] ,dx, where [.] denote… - Vidyadip

MCQ

The value of the integral $\int\limits_0^{0.9} {[ - 2[x]]\,dx,} $ where $[.]$ denotes the greatest integer function is

A
$0.9$
B
$1.8$
C
$-0.9$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
Since $\int\limits_0^a {\left[ x \right]} = 0$ where $0 \le a \le 1$

$\therefore \int\limits_0^{0.9} {\left[ {x - 2\left[ x \right]} \right]} dx = 0$

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