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

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

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

int_(0)^( pi/4)(cos x)/(4-sin^(2)x)*dx

int_(0)^( pi/4)(cos x)/(4-sin^(2)x)*dx

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

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

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

Let u=int_(0)^((pi)/(4))((cos x)/(sin x+cos x))^(2)dx and v=int_(0)^((pi)/(4))((sin x+cos x)/(cos x))^(2)dx Find the value of (v)/(u)