Let the function f satisfies \(f\left( x \right) + 2f\left( {\frac{1}{x}} \right) = {x^2},\;x \ne 0\).
The value of the integral \(\mathop \smallint \limits_1^2 {x^2}f\left( x \right)dx\) is1
\(\frac{{ - 21}}{15}\)
2
\(\frac{{ - 21}}{3}\)
3
\(\frac{21}{5}\)
4
\(\frac{21}{3}\)