Answer
$-\sqrt{ 9-x^2}+C$
Work Step by Step
Let us consider $u = 9-x^2 $
and $du=-2x dx $
Now, the given integral becomes:
$\int \dfrac{-1}{2}[\dfrac{-2x}{ \sqrt{9-x^2}} d x = \dfrac{-1}{2} \int \dfrac{1}{\sqrt u} du$
Now, integrate and plug in $u = 9-x^2 $:
$-u^{1/2}+C=-\sqrt{ 9-x^2}+C$
