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Câu hỏi: Nếu $\int\limits_{2}^{3}{f\left( x \right)\text{d}x=5}$ và $\int\limits_{2}^{3}{g\left( x \right)\text{d}x=-1}$ thì $\int\limits_{2}^{3}{\left[ f\left( x \right)-g\left( x \right)-2x \right]\text{d}x}$ bằng
A. $6$.
B. $5$.
C. $11$.
D. $1$.
A. $6$.
B. $5$.
C. $11$.
D. $1$.
Ta có: $\int\limits_{2}^{3}{\left[ f\left( x \right)-g\left( x \right)-2x \right]\text{d}x}$ $=$ $\int\limits_{2}^{3}{f\left( x \right)\text{d}x}-\int\limits_{2}^{3}{g\left( x \right)\text{d}x}-\int\limits_{2}^{3}{2x\text{d}x}$ $=$ $5+1-{{x}^{2}}\left| \begin{aligned}
& 3 \\
& 2 \\
\end{aligned} \right.=6-5=1$.
& 3 \\
& 2 \\
\end{aligned} \right.=6-5=1$.
Đáp án D.