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Câu hỏi: Cho $\int\limits_{0}^{1}{\left[ f\left( x \right)-2g\left( x \right) \right]dx}=12$ và $\int\limits_{0}^{1}{g\left( x \right)dx}=5$, khi đó $\int\limits_{0}^{1}{f\left( x \right)dx}$ bằng
A. $-2$.
B. 12.
C. 22.
D. 2.
A. $-2$.
B. 12.
C. 22.
D. 2.
Ta có $\int\limits_{0}^{1}{\left[ f\left( x \right)-2g\left( x \right) \right]dx}=\int\limits_{0}^{1}{f\left( x \right)dx}-2\int\limits_{0}^{1}{g\left( x \right)dx}$
$\Rightarrow \int\limits_{0}^{1}{f\left( x \right)dx}=\int\limits_{0}^{1}{\left[ f\left( x \right)-2g\left( x \right) \right]dx}+2\int\limits_{0}^{1}{g\left( x \right)dx}=12+2.5=22$.
$\Rightarrow \int\limits_{0}^{1}{f\left( x \right)dx}=\int\limits_{0}^{1}{\left[ f\left( x \right)-2g\left( x \right) \right]dx}+2\int\limits_{0}^{1}{g\left( x \right)dx}=12+2.5=22$.
Đáp án C.