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Câu hỏi: Cho $\int\limits_{1}^{3}{\left[ f\left( x \right)-2 \right]dx}=12$. Giá trị của $\int\limits_{1}^{3}{f\left( x \right)dx}$ bằng
A. $8$.
B. $20$.
C. $10$.
D. $16$.
Ta có $\int\limits_{1}^{3}{\left[ f\left( x \right)-2 \right]dx}=\int\limits_{1}^{3}{f\left( x \right)dx}-\int\limits_{1}^{3}{2dx}=\int\limits_{1}^{3}{f\left( x \right)dx}-2x\left| \begin{aligned}
& 3 \\
& 1 \\
\end{aligned} \right.=\int\limits_{1}^{3}{f\left( x \right)dx}-4$
$\Rightarrow \int\limits_{1}^{3}{f\left( x \right)dx}=\int\limits_{1}^{3}{\left[ f\left( x \right)-2 \right]dx}+4=12+4=16$
A. $8$.
B. $20$.
C. $10$.
D. $16$.
Ta có $\int\limits_{1}^{3}{\left[ f\left( x \right)-2 \right]dx}=\int\limits_{1}^{3}{f\left( x \right)dx}-\int\limits_{1}^{3}{2dx}=\int\limits_{1}^{3}{f\left( x \right)dx}-2x\left| \begin{aligned}
& 3 \\
& 1 \\
\end{aligned} \right.=\int\limits_{1}^{3}{f\left( x \right)dx}-4$
$\Rightarrow \int\limits_{1}^{3}{f\left( x \right)dx}=\int\limits_{1}^{3}{\left[ f\left( x \right)-2 \right]dx}+4=12+4=16$
Đáp án D.