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

Prove that (pi)/(6)

Prove that: 4leint_1^3sqrt(3+x^3)dxle2sqrt(30)

Prove that :int_(0)^((pi)/(2))sqrt(1-sin2x)dx=2(sqrt(2)-1)

Prove that 4le int_(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30 .

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

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)

Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)

sqrt(x^(2)+6x-4)dx