Prove that : `int_(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0`

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

Prove that : int_(0)^(pi) sin^(2) x . cos x dx =0

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

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

int_(0)^(pi) [2sin x]dx=

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

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

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

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

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