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

Explanation

`\int_{a}^{b} \frac{1}{(1+x^{2})} d x=[\tan ^{-1} x]_{a}^{b} `

`\Rightarrow \int_{a}^{b} \frac{1}{(1+x^{2})}=[\tan ^{-1} x]_{-1}^{1} `


`\Rightarrow[\tan ^{-1}(1)-\tan ^{-1}(-1)] `


`\Rightarrow[\frac{\pi}{4}-(-\frac{\pi}{4})]`


`\Rightarrow \frac{\pi}{4}+\frac{\pi}{4}=\frac{\pi}{2}`