if `int_0^k (dx)/(2+8x^2)=pi/16` then find the value of `k`

Explanation

`int_(0)^(h)(1)/(2+8x^(2))dx=(pi)/(16)`
`rArr" "(1)/(8)int_(0)^(h)(1)/(x^(2)+(1//2)^(2))dx=(pi)/(16)`
`rArr" "(1)/(8)xx(1)/(1//2)[tan^(-1)((x)/(1//2))]_(0)^(h)=(pi)/(16)`
`rArr" "(1)/(4)[tan^(-1)2x]_(0)^(h)=(pi)/(16)`
`rArr" "[tan^(-1)2h- tan^(-1)0]=(pi)/(4)`
`rArr" "tan^(-1)2h=(pi)/(4)`
`rArr" "tan^(-1)2h=tan^(-1)1`
`rArr" "2h=1`
`rArr" "h=(1)/(2)`.