0-1-1-3-4x-4x-2-dx-

Question Number 95673 by Rio Michael last updated on 26/May/20

\int_{0}^{1} \frac{1}{\sqrt{3 + 4 x - 4 x^{2}}} d x = ?

Commented by Tony Lin last updated on 26/May/20

\int_{0}^{1} \frac{1}{\sqrt{3 + 4 x - 4 x^{2}}} d x

= \int_{0}^{1} \frac{1}{\sqrt{- 4 (x^{2} - x + \frac{1}{4}) + 4}} d x

= \frac{1}{2} \int_{0}^{1} \frac{1}{\sqrt{1 - {(x - \frac{1}{2})}^{2}}} d x

= {[\frac{1}{2} {s i n}^{- 1} (x - \frac{1}{2})]}_{0}^{1}

= \frac{π}{6}

Commented by Rio Michael last updated on 26/May/20

thanks