\(\int \limits_{\frac{1}{4}}^1 \frac{d x}{\sqrt{-x^2-2 x+3}}=\)
Answer & explanation
Correct answer: option 4
\(\int \limits_{\frac{1}{4}}^1 \frac{d x}{\sqrt{4-(x+1)^2}}⇒\begin{pmatrix}sin^{_1}\frac{x+1}{2}\end{pmatrix}_{\frac{1}{4}}^1⇒\frac{\pi}{2}-sin^{-1}(\frac{5}{8})\)
\(⇒cos^{-1}(\frac{5}{8})\)
Option D is correct.