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Question
\[\int\sqrt{3 - x^2} \text{ dx}\]
Sum
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Solution
\[\text{ Let I } = \int\sqrt{3 - x^2}\text{ dx}\]
\[ = \int\sqrt{\left( \sqrt{3} \right)^2 - x^2}\text{ dx} \]
\[ = \frac{x}{2}\sqrt{\left( \sqrt{3} \right)^2 - x^2} + \frac{\left( \sqrt{3} \right)^2}{2} \sin^{- 1} \left( \frac{x}{\sqrt{3}} \right) + C\]
\[ = \frac{x}{2} \sqrt{3 - x^2} + \frac{3}{2} \sin^{- 1} \left( \frac{x}{\sqrt{3}} \right) + C\]
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