Prove that `pi/6 lt int_0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))`

Prove that pi/6leint_0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt(2))

Prove that ln 2 lt int_(0)^(1)(dx)/(sqrt(1+x^(4))) lt (pi)/2)

int_(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

Prove that (pi)/(4)

int_(0)^(pi//6) sqrt(1-sin 2x) dx

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

int_(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)/(4)

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)