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

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

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

If I_(1)=int_(0)^(pi//2)log (sin x)dx and I_(2)=int_(0)^(pi//2)log (sin 2x)dx , then

int_(0)^( pi/2)ln(sin^(2)x cos x)dx

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 .

int_(0)^((pi)/(2))log(sin2x)dx

Show that int_(0)^((pi)/(2))log(sin2x)dx=-(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)