(D) Let $I = \int_{0}^{0.9} [x - 2[x]] \, dx$. Since $0 \le x < 0.9$,the greatest integer function $[x] = 0$. Substituting $[x] = 0$ into the integral

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(D) Let $I = \int_{0}^{0.9} [x - 2[x]] \, dx$. Since $0 \le x Substituting $[x] = 0$ into the integral,we get: $I = \int_{0}^{0.9} [x - 2(0)] \, dx = \int_{0}^{0.9} [x] \, dx$. Since $0 \le x Therefore,$I = \int_{0}^{0.9} 0 \, dx = 0$.

Class 12 Mathematics 7-2.Definite Integral Fundamental definite integration

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The value of the integral $\int_{0}^{0.9} [x - 2[x]] \, dx$,where $[.]$ denotes the greatest integer function,is

AIEEE 2012 All AIEEE

A
$0.9$
B
$1.8$
C
$-0.9$
D
$0$

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The value of the integral $\int_{0}^{0.9} [x - 2[x]] \, dx$,where $[.]$ denotes the greatest integer function,is

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