Evaluate _0^a d x a^2-x^2 . - Vidyadip

Question

Evaluate $\int_0^a \frac{d x}{\sqrt{a^2-x^2}}$.

✓

Answer

Let
$
\text { } \begin{aligned}
I & =\int_0^a \frac{d x}{\sqrt{a^2-x^2}} \\
=\left(\sin ^{-1} \frac{x}{a}\right)_0^a & =\sin ^{-1} \frac{a}{a}-\sin ^{-1}(0) \\
& =\sin ^{-1} 1-\sin ^{-1} 0 \\
& =\frac{\pi}{2}-0=\frac{\pi}{2} \text { Ans. }
\end{aligned}
$

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