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Câu hỏi: Cho $\int\limits_{2}^{5}{f\left( x \right)\text{d}x}=10$. Khi đó $\int\limits_{5}^{2}{\left[ 2-4f\left( x \right) \right]\text{d}x}$ bằng
A. $32$.
B. $34$.
C. $36$.
D. $40$.
A. $32$.
B. $34$.
C. $36$.
D. $40$.
Ta có $\int\limits_{5}^{2}{\left[ 2-4f\left( x \right) \right]\text{d}x}=2\int\limits_{5}^{2}{\text{d}x}-4\int\limits_{5}^{2}{f\left( x \right)\text{d}x}=2x\left| _{\begin{smallmatrix}
\\
5
\end{smallmatrix}}^{\begin{smallmatrix}
2 \\
\end{smallmatrix}} \right.+4\int\limits_{2}^{5}{f\left( x \right)\text{d}x}=2.\left( 2-5 \right)+4.10=34$.
\\
5
\end{smallmatrix}}^{\begin{smallmatrix}
2 \\
\end{smallmatrix}} \right.+4\int\limits_{2}^{5}{f\left( x \right)\text{d}x}=2.\left( 2-5 \right)+4.10=34$.
Đáp án B.