use subtitution x=a sinθ to find ∫(1/( (√(9−x^2 ))))


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Question Number 125845 by joki last updated on 14/Dec/20

$u s e s u b t i t u t i o n x = a s i n θ t o f i n d \int \frac{1}{\sqrt{9 - x^{2}}}$
	Answered by MJS_new last updated on 14/Dec/20

	$\int \frac{d x}{\sqrt{9 - x^{2}}} =$ $[x = 3 \sin θ \Leftrightarrow θ = \arcsin \frac{x}{3} \to d x = \sqrt{9 - x^{2}} d θ]$ $= \int d θ = θ = \arcsin \frac{x}{3} + C$
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