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I=int(0)^((pi)/(2))log sin pi dx-theta...

I=int_(0)^((pi)/(2))log sin pi dx-theta

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int_(0)^((pi)/(2))log(sin x)dx

STATEMENT 1: int_(0)^((pi)/(4))log(1+tan theta)d theta=(pi)/(8)log2 STATEMENT 2:int_(0)^((pi)/(2))log sin theta d theta=-pi log2

int_(0)^((pi)/(2))log(sin2x)dx

If int_(0)^((pi)/(2))log sin theta d(theta)=k, then find the value of int_(0)^((pi)/(2))((theta)/(sin theta))^(2)d(theta) in terms of k

Evaluate: int_(0)^((pi)/(2)) log (sin x) dx

int_(0)^(pi//2) log sin x dx =

int_(0)^((pi)/(2))log(tanx)dx

int_(0)^((pi)/(4))log(sin2 theta)d theta=-((pi)/(4))log((1)/(2))

int_(0)^((pi)/(2))log sin xdx=int_(0)^((pi)/(2))log cos xdx=(1)/(2)(pi)log((1)/(2))

If f(x)=int_(0)^((pi)/(2))(ln(1+x sin^(2)theta))/(sin^(2)theta)d theta,x>=0 then :