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int(0)^( pi/2)log(sin x)dx...

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

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Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

If I_(1) = int_(0)^(pi//2)ln (sin x)dx , I_(2)=int_(-pi//4)^(pi//4)ln (sin x + cos x)dx , then :

Prove that: int_(0)^( pi/2)log(sin^(3)x cos^(4)x)backslash dx=-(7 pi)/(2)log2

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

Consider is int_(0)^(pi//2) ln (sinx)dx equal to ? What is int_(0)^(pi//2) ln (cos x) dx equal to ?

If int_(0)^((pi)/2)log(cosx)dx=-(pi)/2log2 , then int_(0)^((pi)/2)log(cosecx)dx=