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))log(sin2x)dx

If I_(1)=int_(0)^(pi//2) x sin x dx and I_(2) = int_(0)^(pi//2) x cos x dx ,then which one of the following is true ?

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

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

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 :

int_(0)^( pi)cos2x*log(sin x)dx

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

Suppose _((pi)/(2))cos(pi sin^(2)x)dx and I_(2)int_(0)^(3)cos(2 pi sin^(2)x)dx and I_(3)=int_(0)^((pi)/(2))cos(pi sin x)dx, then

If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to