Đáp án:
\[A\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left\{ \begin{array}{l}
u = x\\
v' = {e^{3x}}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
u' = 1\\
v = \frac{{{e^{3x}}}}{3}
\end{array} \right.\\
\int\limits_0^1 {x.{e^{3x}}dx} = \mathop {\left. {x.\frac{{{e^{3x}}}}{3}} \right|}\nolimits_0^1 - \int\limits_0^1 {1.\frac{{{e^{3x}}}}{3}dx} \\
= \frac{{{e^3}}}{3} - \mathop {\left. {\frac{1}{9}.{e^{3x}}} \right|}\nolimits_0^1 \\
= \frac{{{e^3}}}{3} - \frac{{{e^3}}}{9} + \frac{1}{9}\\
= \frac{2}{9}{e^3} + \frac{1}{9}\\
\Rightarrow a = \frac{2}{9};\,\,\,b = \frac{1}{9} \Rightarrow a - b = \frac{1}{9}
\end{array}\)
