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The function f(x)=int(0)^(x) log (|sin t...

The function `f(x)=int_(0)^(x) log _(|sin t|)(sin t + (1)/(2)) dt`, where `x in (0,2pi)`, then `f(x)` strictly increases in the interval

A

`((pi)/(6),(5pi)/(6))`

B

`((5pi)/(6),2pi)`

C

`((pi)/(6),(7pi)/(6))`

D

`((5pi)/(6),(7pi)/(6))`

Text Solution

Verified by Experts

The correct Answer is:
D
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