​ Find: ∫ dx/ √4x - x^2

Question

Find:

\(\int \frac{dx}{\sqrt{4x - x^2}}\)

Answer 1

\(\int \frac{dx}{\sqrt{4x - x^2}}\)

\(= \int \frac{dx}{\sqrt{4 - 4+4x - x^2}}\)

\(= \int \frac{dx}{\sqrt{4 - (x-2)^2}}\)

\(= sin^{-1} \left(\frac{x -2}{2}\right) + C\)    \(\left(\because\int \frac{dx}{\sqrt{a^2 - x^2}} = sin^{-1} \frac xa + C\right)\)