Ta thấy, với \(0 < x < 1\) thì \(x - {x^3} > 0\).
Với \( - 1 < x < 0\) thì \(x - {x^3} < 0\).
\( \Rightarrow \int\limits_{ - 1}^1 {\left| {x - {x^3}} \right|dx} \)\( = \int\limits_{ - 1}^0 {\left( { - x + {x^3}} \right)dx} + \int\limits_0^1 {\left( {x - {x^3}} \right)dx} \) \( = \left. {\left( { - \dfrac{{{x^2}}}{2} + \dfrac{{{x^4}}}{4}} \right)} \right|_{ - 1}^0 + \left. {\left( {\dfrac{{{x^2}}}{2} - \dfrac{{{x^4}}}{4}} \right)} \right|_0^1\)
\( = \dfrac{1}{2} - \dfrac{1}{4} + \dfrac{1}{2} - \dfrac{1}{4} = \dfrac{1}{2}\).
Chọn A.
