Evaluate the following definite integrals: _ -2 ^ 1 2 1 1-x^2 dx - Vidyadip

Question

Evaluate the following definite integrals:
$\int_{-2}\limits^{\frac{1}{2}}\frac{1}{\sqrt{1-\text{x}^2}} \text{ dx}$

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Answer

Let $\int_{-2}\limits^{\frac{1}{2}}\frac{1}{\sqrt{1-\text{x}^2}} \text{ dx}$ Then,
$\text{I}=\big[\sin^{-1}\text{x}\big]^{\frac{1}{2}}_0$
$\Rightarrow\text{I}=\sin^{-1}\frac{1}{2}-\sin^{-1}0$
$\Rightarrow\text{I}=\frac{\pi}{6}-0$
$\Rightarrow\text{I}=\frac{\pi}{6}$

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