Question
Integrate the function $\sqrt {4 - {x^2}} $

Answer

$\int {\sqrt {4 - {x^2}} dx} $

$ = \int {\sqrt {2^2 - {x^2}} dx} $

$= \frac{x}{2}\sqrt {{2^2} - {x^2}} + \frac{{{2^2}}}{2}{\sin ^{ - 1}}\frac{x}{2} + c$

$\left[ {\because \int {\sqrt {{a^2} - {x^2}} dx} } \right.$ $\left. { = \frac{x}{2}\sqrt {{a^2} - {x^2}} + \frac{{{a^2}}}{2}{{\sin }^{ - 1}}\frac{x}{a}} \right]$

$= \frac{x}{2}\sqrt {4 - {x^2}} + 2{\sin ^{ - 1}}\frac{x}{2} + c$

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