Integrate the function in Exercise. 4-x^2 - Vidyadip

Question

Integrate the function in Exercise.
$\sqrt{4-\text{x}^2}$

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Answer

$\int\sqrt{4-\text{x}^2}\text{dx}=\int\sqrt{2^2-\text{x}^2}\text{dx}$
$=\frac{\text{x}}{2}\sqrt{2^2-\text{x}^2}+\frac{2^2}{2}\sin^{-1}\frac{\text{x}}{2}+\text{C}$
$\Bigg[\therefore\ \sqrt{\text{a}^2-\text{x}^2}\text{dx}=\frac{\text{x}}{2}\sqrt{\text{a}^2-\text{x}^2}+\frac{\text{a}^2}{2}\sin^{-1}\frac{\text{x}}{\text{a}}\Bigg]$
$=\frac{\text{x}}{2}\sqrt{4-\text{x}^2}+2\sin^{-1}\frac{\text{x}}{2}+\text{C}$

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