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int(0)^( pi/2)f(sin2x)sin xdx=sqrt(2)int...

int_(0)^( pi/2)f(sin2x)sin xdx=sqrt(2)int_(0)^( pi/4)f(cos2x)cos xdx

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Show that, int_(0)^((pi)/(2))f(sin2x)sinxdx=sqrt(2)int_(0)^((pi)/(4))f(cos2x)cosxdx

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 .

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 .

The value of the integral sqrt2 int_0^(pi/2) f(sin2x) sinx dx=A (sqrt2/9) int_0^(pi/4) f(cos2x)cosx dx then the value of A is

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