Evaluate: _0^1 1 1+x^2 d x - Vidyadip

Question

Evaluate: $\int_0^1 \frac{1}{1+x^2} d x$

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Answer

$\int_0^1 \frac{1}{1+x^2} d x=\left[\tan ^{-1} x\right]_0^1$
$=\tan ^{-1} 1-\tan ^{-1} 0$
$=\frac{\pi}{4}-0$
$=\frac{\pi}{4}$

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