The value of `int_(0)^(pi//2)` log (sinx) dx is

Options

A. `(pi)/(2) ` log 2
B. `pi` log 2
C. `-(pi)/(2)` log 2
D. `2pi` log 2

Answer

A

Explanation

Let `I = int _(0)^(pi//2) log (cosec x) dx`
`= int_(0)^(pi//2) log ((1)/(sinx)) dx`
` = - int_(0)^(pi//2) log sin x `dx
`= (pi)/(2) ""log 2`
`[because int_(0)^(pi//2) log sin x dx = - (pi)/(2)""log 2`]