Evaluate _0^ 1 dx 1 + x^ 2 - Vidyadip

Question

$ \text{Evaluate} \int\limits_0^{1} \frac{dx}{1 + x^{2}}$

✓

Answer

$\int\limits_0^{1} \frac{dx}{1 + x^{2}}=\big[\tan^{-1}\text{x}\big]^1_0$

$\tan^{-1}\perp-\tan^{-1}0$

$=\frac{\pi}{4}-0$

$=\frac{\pi}{4}$

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