Practicing Success
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\(\int \limits_{\frac{1}{4}}^1 \frac{d x}{\sqrt{-x^2-2 x+3}}=\) |
sin-1\((\frac{1}{4})\) sin-1\((\frac{3}{4})\) sin-1\((\frac{5}{8})\) cos-1\((\frac{5}{8})\) |
cos-1\((\frac{5}{8})\) |
\(\int \limits_{\frac{1}{4}}^1 \frac{d x}{\sqrt{4-(x+1)^2}}⇒\begin{pmatrix}sin^{_1}\frac{x+1}{2}\end{pmatrix}_{\frac{1}{4}}^1⇒\frac{\pi}{2}-sin^{-1}(\frac{5}{8})\) \(⇒cos^{-1}(\frac{5}{8})\) Option D is correct. |
