If `int_0^a1/(4+x^2)dx=pi/8` , find the value of `adot`

Explanation

given that `int_{0}^{a} frac{1}{4+x^{2}} d x=frac{pi}{8}`

We need to find the value of `a`.

Let `I=int_{0}^{a} frac{1}{4+x^{2}} d x=frac{pi}{8}`

Thus, `I=frac{1}{2}(tan ^{-1}(frac{x}{2}))_{0}^{a}=frac{pi}{8}`


`Rightarrow frac{1}{2} tan ^{-1}(frac{a}{2})=frac{pi}{8}`



`Rightarrow tan ^{-1}(frac{a}{2})=frac{pi}{4} `

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