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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate: $\int \limits_0^{\large\frac{2}{3}}$$ \large\frac{dx}{4+ 9x^2}$

\[\begin {array} {1 1} (a)\;\frac{\pi}{24} \\ (b)\;\frac{\pi}{12} \\ (c)\;\frac{\pi}{6} \\ (d)\;\frac{\pi}{18} \end {array}\]

1 Answer

$\large\frac{1}{9} x \int \limits_0^{\large\frac{2}{3}} \large\frac{dx}{(2/3)^2 +x^2} $
=> $\large\frac{1}{9} \times \frac{3}{2}$$ \bigg[ \tan^{-1} (\frac{3x}{2})\bigg]_0^{\large\frac{2}{3}}$
=> $\large\frac{1}{6} $$[\tan^{-1}[1] -\tan^{-1}[0]]$
=>$\large\frac{\pi}{24}$
Hence a is the correct answer.
answered Dec 16, 2013 by meena.p
 
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