Question

If $\left[t\right]$ stands for greatest integer function of $t$,then ${\int }_0^{\pi /4}\left[\tan x\right]dx=$

• A. $\frac{\pi }{2}$
• B. $0$
• C. $\frac{\pi }{4}$
• D. $2\pi$

Answer 1

Answer: (B)

$0$

In $(0,\frac{\pi }{4})$ the vale of $tanx$ varies from $(0,1)$.

so, value of $\left[tanx\right]$ = $0$ for interval $(0,\frac{\pi }{4})$

hence, ${\int }_0^{\pi /4}\left[\tan x\right]dx=0$.