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int(0)^( pi/2)log(sin t)dt...

int_(0)^( pi/2)log(sin t)dt

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If I_(1)=int_(0)^(pi//2)log (sin x)dx and I_(2)=int_(0)^(pi//2)log (sin 2x)dx , then

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

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

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

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

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

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

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