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

Explanation

For `nge1`and `-1gexge1`, we have
`1gesqrt(1-x^(2n))ge sqrt(1-x^(2))`
or `int_(0)^(1//2)dxleint_(0)^(1//2)(dx)/(sqrt(1-x^(2n)))le int_(0)^(1//2)(dx)/(sqrt(1-x^(2)))=[sin^(-1)x]_(0)^(1//2)`
or `1/2 le int_(0)^(1//2)(dx)/(sqrt(1-x^(2n)))le(pi)/6`