Evaluate `int_(0)^(pi//2) x cot xdx`

Evaluate int_(0)^(pi//2)cos^(4)xdx

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

Evaluate : int_(0)^(pi//2)cos^(9)xdx

Evaluate int_(0)^(pi//2)lnsin2xdx

Evaluate int_(0)^(pi) cotx.cos2xdx

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

Prove that : int_(0)^(pi//2) x . cot x dx =(pi)/(2)log 2

Evaluate int_0^(pi/2) log sin xdx

Evaluate : int_(0)^(pi//2)sin^(8)xdx

int_(0)^( pi/2)x sec^(2)xdx