Question Number 125845 by joki last updated on 14/Dec/20 | ||
$${use}\:{subtitution}\:{x}={a}\:{sin}\theta\:{to}\:{find}\:\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }} \\ $$ | ||
Answered by MJS_new last updated on 14/Dec/20 | ||
$$\int\frac{{dx}}{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}= \\ $$$$\:\:\:\:\:\left[{x}=\mathrm{3sin}\:\theta\:\Leftrightarrow\:\theta=\mathrm{arcsin}\:\frac{{x}}{\mathrm{3}}\:\rightarrow\:{dx}=\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }{d}\theta\right] \\ $$$$=\int{d}\theta=\theta=\mathrm{arcsin}\:\frac{{x}}{\mathrm{3}}\:+{C} \\ $$ | ||