" 9."int_(0)^( pi)x log sin xdx=(-pi^(2))/(2)log2

int_(0)^( pi)log xdx

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

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

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

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2

"int_(0)^( pi)x sin^(2)xdx

Evaluate int_(0)^( pi)x log sin xdx

int_(0)^( pi)cos2x*log(sin x)dx

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