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

Question

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

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Answer

$\int_0^1 \frac{1}{\sqrt{1-x^2}} d x=\left[\sin ^{-1} x\right]_0^1$
$=\sin ^{-1}(1)-\sin ^{-1}(0)$
$=\frac{\pi}{2}-0$
$=\frac{\pi}{2}$

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