$\sqrt {4 - {x^2}}$
$\sqrt {4 - {x^2}}$
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NCERT & Exemplar
Let $I = \int {\sqrt {4 - {x^2}} dx} = \int {\sqrt {{{\left( 2 \right)}^2} - {x^2}} dx}$
$= \left[ {\cfrac{x}{2}\sqrt {{{\left( 2 \right)}^2} - {x^2}} + \cfrac{4}{2}{{\sin }^{ - 1}}\left( {\cfrac{x}{2}} \right)} \right] + C$
$= \cfrac{{x\sqrt {4 - {x^2}} }}{2} + \cfrac{4}{2}{\sin ^{ - 1}}\left( {\cfrac{x}{2}} \right) + C = \cfrac{{x\sqrt {4 - {x^2}} }}{2} + 2{\sin ^{ - 1}}\left( {\cfrac{x}{2}} \right) + C$
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