By the linearity of integration, we have
∫ 2 3 ( 6 f ( x ) − 3 g ( x ) ) d x = 6 ∫ 2 3 f ( x ) d x − 3 ∫ 2 3 g ( x ) d x . {\displaystyle \int _{2}^{3}(6f(x)-3g(x))\,dx=6\int _{2}^{3}f(x)\,dx-3\int _{2}^{3}g(x)\,dx.}
Using the given information, we evaluate
6 ∫ 2 3 f ( x ) d x − 3 ∫ 2 3 g ( x ) d x = 6 ( − 1 ) − 3 ( 5 ) = − 21 {\displaystyle 6\int _{2}^{3}f(x)\,dx-3\int _{2}^{3}g(x)\,dx=6(-1)-3(5)=\color {blue}-21} .
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