`I=int_(0)^( pi)(sin^(2)(x/2)-cos^(2)(x/2)) dx`

If I=int_(0)^( pi)x(sin^(2)(sin x)+cos^(2)(cos x))dx , then [l]= (where) [.] denotes the greatest integer function

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

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

int_(-pi)^(pi)sin^(2)x.cos^(2)x dx=

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

int_(0)^( pi)(sin x)/(1+cos^(2)x)dx =

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

Find I=int_(0)^((3 pi)/(2))cos^(4)(3x)sin^(2)(6x)dx

Prove that: int_(0)^(2 pi)(x sin^(2n)x)/(sin^(2n)+cos^(2n)x)dx=pi^(2)

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to