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int(0)^( pi/4)cot^(2)x*dx...

int_(0)^( pi/4)cot^(2)x*dx

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If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx. then

If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx. then

int_(pi//4)^(pi//2)cot^(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//2)x cot x dx=(pi)/(2)(log2)

I_(n)=int_(pi/4)^(pi/2)(cot^(n)x)dx , then :

int_(0)^(pi//4) cot x. " cosec"^(2) x dx