use-subtitution-x-a-sin-to-find-1-9-x-2-

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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