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प्रश्न
\[\int\sqrt{2ax - x^2} \text{ dx}\]
योग
उत्तर
\[\text{ Let I }= \int\sqrt{2ax - x^2}\text{ dx}\]
\[ = \int\sqrt{a^2 + 2ax - x^2 - a^2}\text{ dx}\]
\[ = \int \sqrt{a^2 - \left( x^2 - 2ax + a^2 \right)}\text{ dx}\]
\[ = \int\sqrt{a^2 - \left( x - a \right)^2}\text{ dx}\]
\[ = \left( \frac{x - a}{2} \right) \sqrt{2ax - x^2} + \frac{a^2}{2} \sin^{- 1} \left( \frac{x - a}{a} \right) + C\]
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