_0^ 2/3 dx 4 + 9 x^2 = - Vidyadip

MCQ

$\int_0^{2/3} {\frac{{dx}}{{4 + 9{x^2}}} = } $

A
$\frac{\pi }{{12}}$
✓
$\frac{\pi }{{24}}$
C
$\frac{\pi }{4}$
D
$0$

✓

Answer

Correct option: B.

$\frac{\pi }{{24}}$

b
(b) $\int_0^{2/3} {\frac{{dx}}{{4 + 9{x^2}}} = \frac{1}{9}\int_0^{2/3} {\frac{{dx}}{{{{(2/3)}^2} + {x^2}}}} } $

$ = \frac{1}{9} \times \frac{1}{{2/3}}\left( {{{\tan }^{ - 1}}\frac{x}{{2/3}}} \right)_0^{2/3} $

$= \frac{\pi }{4} \times \frac{1}{6} = \frac{\pi }{{24}}$.

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