Giải thích các bước giải:
Do f(x) là hàm số chẵn nên \(f\left( x \right) = f\left( { - x} \right)\)
\(\begin{array}{l}
\int\limits_{ - a}^a {f\left( x \right)dx} = \int\limits_{ - a}^0 {f\left( x \right)dx} + \int\limits_0^a {f\left( x \right)dx} \\
t = - x \Rightarrow \left\{ \begin{array}{l}
dt = - dx\\
x = - a \Rightarrow t = a\\
x = 0 \Rightarrow t = 0
\end{array} \right.\\
\Rightarrow \int\limits_{ - a}^0 {f\left( x \right)dx} = \int\limits_a^0 {f\left( { - t} \right).\left( { - dt} \right)} = - \int\limits_0^a {f\left( { - t} \right)\left( { - dt} \right)} = \int\limits_0^a {f\left( { - t} \right)dt} = \int\limits_0^a {f\left( t \right)dt = \int\limits_0^a {f\left( x \right)dx} } \,\,\,\,\left( {f\left( { - t} \right) = f\left( t \right)} \right)\\
\Rightarrow \int\limits_{ - a}^a {f\left( x \right)dx} = \int\limits_{ - a}^0 {f\left( x \right)dx} + \int\limits_0^a {f\left( x \right)dx} = 2.\int\limits_0^a {f\left( x \right)dx}
\end{array}\)
