`P rov et h a t1/2lt=int_0^(1/2)(dx)/(sqrt(1-x^(2n)))lt=pi/6forngeq1.`

P rov et h a t4lt=int_1^3sqrt(3+x^2)lt=4sqrt(3)

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

Evaluate int_0^((pi)/(2))(dx)/(1+sqrt(tanx))

Prove that 0 lt int_0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

Evaluate: int_0^1(2-x^2)/((1+x)sqrt(1-x^2))dx

Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these

If x lt 0 , the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x