`int_(pi/4)^( pi/2)cos2x log sin xdx`

int_(0)^(pi) cos 2x . Log (sinx) dx

Evaluate : int_(-pi/2)^(pi/2)xcos^2 xdx

Evaluate : int_(-pi/2)^(pi/2)xcos^2 xdx

int_(0)^(pi/2)cos^2x sin^2xdx

int_(-pi/2)^(pi/2) sin x*cos^2 xdx

(v) int_(-pi/2)^(pi/2) sin x*cos^2 xdx

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

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_(-pi/4)^(pi/4)sec^(2)xdx

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