Evaluate the following integrals: ^1_01 1+x^2 dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$

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Answer

$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$
$=\big[\tan^{-1}\text{x}\big]^1_0$
$=\tan^{-1}1-\tan^{-1}0$
$=\frac{\pi}{4}-0$
$=\frac{\pi}{4}$

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