Evaluate the following definite integral: `int_0^(1/2) 1/sqrt(1+x^2)dx`

Explanation

`int_{a}^{b} frac{1}{sqrt{(1-x^{2})}} d x=[-cos ^{-1} x]_{a}^{b}`

`int_{0}^{1 / 2} frac{1}{sqrt{(1-x^{2})}}=[-cos ^{-1} x]_{0}^{1 / 2}`

`Rightarrow-[cos ^{-1} (1 / 2)-cos ^{-1} 0]`

`Rightarrow-[frac{pi}{3}-frac{pi}{2}]`

`Rightarrow[frac{pi}{6}]`

`int_{0}^{1 / 2} frac{1}{sqrt{(1-x^{2})}}=[frac{pi}{6}]`