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