If `int_(0)^(K)(cos(x)dx)/(1+sin^(2)(x))=(pi)/(4)` then K=

int_(0)^(pi)(cos^(4)x-sin^(4)x)dx=

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

int_(0)^(pi//2)(cos^(4)x)/((sin^(4)x+cos^(4)x))dx=(pi)/(4)

If int_(0)^(20)sqrt(1-cos pi x)dx=(10k sqrt(2))/(pi), then k is

If int_(0)^(pi//2)sin^(4)x cos^(2)x dx=(pi)/(32) , then int_(0)^(pi//2)sin^(2)x cos^(4)x dx=

int_(0)^(pi//2)(sin x.cos x)/(1+sin^(4)x)dx=

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

Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)