Prove that,
`int_(0)^(6pi)sin^(4)xdx=6int_(0)^(pi)sin^(4)xdx`

int_(0)^(8pi)sin^(6)xdx=8int_(0)^(pi)sin^(6)xdx

int_(0)^( pi)sin^(2)xdx

int_(0)^( pi)sin^(5)xdx

int_(0)^( pi/4)sin^(4)xdx

int_(0)^(2 pi)sin^(3)xdx

int_(0)^(pi//2)sin^(9)xdx=

Show that, int_(0)^(pi)sin^(4)xdx=2int_(0)^((pi)/(2))sin^(4)xdx , hence, find the value of int_(0)^(pi)sin^(4)xdx .

int_(0)^( pi)x sin^(3)xdx

int_(0)^(pi//2)sin^(7)xdx

int_(0)^( pi/4)sin xdx