Answer
\[ = 10\]
Work Step by Step
\[\begin{gathered}
\int_1^4 {\,\left( {3f\,\left( x \right) - 2g\,\left( x \right)} \right)} dx \hfill \\
\hfill \\
split\,\,the\,\,{\text{integrand}} \hfill \\
\hfill \\
= 3\int_1^4 {f\,\left( x \right)\,\,dx} - 2\int_1^4 {g\,\left( x \right)} dx \hfill \\
\hfill \\
use\,\,the\,{\text{ }}data\,from\,\,the\,\,given\,{\text{exercise}} \hfill \\
\hfill \\
= 3\,\left( 6 \right) - 2\,\left( 4 \right) \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= 18 - 8 \hfill \\
\hfill \\
= 10 \hfill \\
\end{gathered} \]
