Question

${\int }_{\frac{\sqrt{2}}{3}}^{\frac{\sqrt{3}}{3}}\frac{dx}{\sqrt{4-9x^2}}dxis$

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{12}$
• C. $\frac{\pi }{24}$
• D. $\frac{\pi }{36}$

Answer 1

The correct option is D $\frac{\pi }{36}$

${\int }_{\frac{\sqrt{2}}{3}}^{\frac{\sqrt{3}}{3}}\frac{dx}{\sqrt{4-9x^2}}=\frac{1}{3}[Si{n}^{-1}\frac{3x}{2}{]}_{\frac{\sqrt{2}}{3}}^{\frac{\sqrt{3}}{3}}=\frac{1}{3}[\frac{\pi }{3}-\frac{\pi }{4}]=\frac{\pi }{36}$