Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
37,\\
\int\limits_0^2 {\left[ {2x + f\left( x \right) - 2g\left( x \right)} \right]dx} \\
= \int\limits_0^2 {2xdx} + \int\limits_0^2 {f\left( x \right)dx} - 2\int\limits_0^2 {g\left( x \right)dx} \\
= \mathop {\left. {{x^2}} \right|}\nolimits_0^2 + 3 - 2.\left( { - 2} \right)\\
= 4 + 3 + 4 = 11\\
38,\\
t = - x \Rightarrow dt = - d\left( x \right)\\
\int {f\left( { - x} \right)dx} = - \int {f\left( t \right).d\left( t \right)} = - \int {f\left( x \right)dx} = {x^2} - 2x + C
\end{array}\)
