What does the fox do!

$\int _{ 0 }^{ x }{ \sqrt { 1-{ (f'(x)) }^{ 2 } } dx } =\int _{ 0 }^{ x }{ f(x)dx }$ Differentiating, $\sqrt { 1-{ (f'(x)) }^{ 2 } } =f(x)$ . Thus, $1-{ (f'(x)) }^{ 2 }={ (f(x)) }^{ 2 }$ . Simplifying, ${ f'(x) }=\sqrt { 1-{ (f(x)) }^{ 2 } }$ . Writing $f(x)$ as $y$ $\frac { dy }{ dx } =\sqrt { 1-{ y }^{ 2 } }$ . Hence, $\frac { dy }{ \sqrt { 1-{ y }^{ 2 } } } =dx$ . Integrating, $\arcsin { y } =x$ . Writing $y$ as $f(x)$ , $\arcsin { f(x) } =x$ . Hence $f(\frac { \pi }{ 3 } )=\frac { \sqrt { 3 } }{ 2 }$