_1^ 3 1 1 + x^2 dx is equal to - Vidyadip

MCQ

$\int_1^{\sqrt 3 } {\frac{1}{{1 + {x^2}}}dx} $ is equal to

✓
$\pi /12$
B
$\pi /6$
C
$\pi /4$
D
$\pi /3$

✓

Answer

Correct option: A.

$\pi /12$

a
(a) $\int_1^{\sqrt 3 } {\frac{1}{{1 + {x^2}}}dx = [{{\tan }^{ - 1}}x]_{\,1}^{\sqrt 3 } = \frac{\pi }{3} - \frac{\pi }{4} = \frac{\pi }{{12}}} $.

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