Question

Find $ \int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,dx} $

• A. $ \frac{1}{2\sqrt{7}}\,\log \,\left| \frac{\sqrt{7+x}}{\sqrt{7-x}} \right|+c $
• B. $ {{\sin }^{-1}}\,\left( \frac{x}{\sqrt{7}} \right)+c $
• C. $ \log |x+\sqrt{{{x}^{2}}-7}|+c $
• D. $ \frac{1}{2\sqrt{7}}\log \,\left| \frac{x-\sqrt{7}}{x+\sqrt{7}} \right|+c $

Answer 1

Answer: (B)

$ \int{\frac{1}{\sqrt{7-{{x}^{2}}}}\,\,dx=\int{\frac{1}{\sqrt{{{(\sqrt{7})}^{2}}-{{x}^{2}}}}\,dx}} $

$={{\sin }^{-1}}\left( \frac{x}{\sqrt{7}} \right)+C $