The value of the integral _0^0.9 [x-2[x]],dx, where [.] denotes the greatest integer funct…

Question

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

Accepted Answer

Since $\int_0^a [x]\,dx = 0$ where $0 \leq a \leq 1$ (as $[x]=0$ throughout):

$\int_0^{0.9}[x-2[x]]\,dx = \int_0^{0.9}[x]\,dx = 0$

Solutions · 1