Question

Find $∫\frac{1}{\sqrt{7−x^2}}dx$

• A. $\frac{1}{2\sqrt{7}}\log â\frac{\sqrt{7+x}}{\sqrt{7−x}}â+c$
• B. ${\sin }^{−1}\left(\frac{x}{\sqrt{7}}\right)+c$
• C. $\log âˆ\pounds x+\sqrt{x^2−7}âˆ\pounds +c$
• D. $\frac{1}{2\sqrt{7}}\log â\frac{x−\sqrt{7}}{x+\sqrt{7}}â+c$

Answer 1

Answer: (B)

$∫\frac{1}{\sqrt{7−x^2}}dx=∫\frac{1}{\sqrt{{(\sqrt{7})}^2−x^2}}dx$

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