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

Evaluate the following integral: int_(-pi//4)^(pi//2)"sin" xdx

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

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

Evaluate int_(-pi/4)^(pi/4) sin^2xdx

Evaluate: int_(0)^((pi)/(2)) 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

Evaluate int_0^(pi/2) log sin xdx

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

If= int_(0)^(pi//2) sin x . log (sin x ) dx = log ((K)/(e)). Then, the value of K is ….

Find the value of int_(0)^(pi//2)cos^(5)x sin ^(7)xdx