int_(0)^( pi/2)x cot xdx=(pi)/(2)(log2)

int_(0)^(pi//2)x cot x dx=(pi)/(2)(log2)

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/2)x sin xdx

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

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

int_(0)^( pi/2)e^(x)xdx=

Show that int_(0)^((pi)/(2))logsinxdx=(pi)/(2)log((1)/(2))=(-pi)/(2)log2

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

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