Find $\huge f$ if $\huge f'(x) = \frac{4}{\sqrt{1-x^2}}$ and $\huge f(\frac{1}{2})=-10$ $\huge \begin{align} f(x) &= 4\sin^{-1}x +C \\ -10 &= 4\sin^{-1}{\frac{1}{2}} + C\\ C &=-4\sin^{-1} \frac{1}{2} -10 \\ f(x) &= 4\sin^{-1}x - \frac{2\pi}{3} - 10 \\ \end{align} $