The value of _ - a ^a 1 x + x^3 dx is - Vidyadip

MCQ

The value of $\int_{ - a}^a {\frac{1}{{x + {x^3}}}dx} $ is

✓
$0$
B
$\int_0^a {\frac{1}{{1 + {x^6}}}\;} dx$
C
$2\int_0^a {\frac{1}{{1 + {x^3}}}\;} dx$
D
$\int_0^a {\frac{1}{{1 + {{(a - x)}^3}}}\;} dx$

✓

Answer

Correct option: A.

$0$

a
(a) Since $\int_{ - a}^a {f(x)} \;dx = 0$,

if $f( - x) = - f(x)$

Therefore, $\int_{ - a}^a {\frac{{dx}}{{x + {x^3}}}} = 0$.

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