Show that `int_(0)^(pi//2)f(sin2x)sin zx dx=sqrt(2) int_(0)^(pi//4)f(cos 2x)cosx dx`.

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

If the function f : [-1,1] to R is continuous and even, then show that int_(0)^(pi//2)f(cos2x)cosxdx=sqrt(2)int_(0)^(pi//4)f(sin2x)cosxdx .

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

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

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

int_(0)^(pi//2) sqrt(1- cos 2x) dx

int_(0)^(pi//2) sqrt(1- cos 2x) dx

int_(0)^(pi/6) sin2x . cosx dx