1.

The value of `int_(0)^(pi//2)` log (sinx) dx isA. `(pi)/(2) ` log 2B. `pi` log 2C. `-(pi)/(2)` log 2D. `2pi` log 2

Answer» Correct Answer - A
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`]


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