Question

The value of integral $\underset{0}{\overset{\pi /4}{\int }}[\sin x+[\cos x+[\tan x+[\sec x\left]\right]\left]\right]dx$ is equal to, (where $[\cdot ]$ denotes the greatest integer function)

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{2\pi }{3}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is B $\frac{\pi }{4}$

Given $I=\underset{0}{\overset{\pi /4}{\int }}[\sin x+[\cos x+[\tan x+[\sec x\left]\right]\left]\right]dx$
$=\underset{0}{\overset{\pi /4}{\int }}[\sin x+[\cos x+[\tan x+1]\left]\right]$
$=\underset{0}{\overset{\pi /4}{\int }}[\sin x+[\cos x+1\left]\right]=\underset{0}{\overset{\pi /4}{\int }}1\cdot dx=\frac{\pi }{4}$