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Câu hỏi: Cho $\int\limits_{0}^{1}{\left( {{x}^{2}}-2x-3f\left( x \right) \right)\text{d}x=1}$. Tính $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$.
A. $\dfrac{-1}{3}$.
B. $\dfrac{-5}{3}$.
C. $\dfrac{-1}{9}$.
D. $\dfrac{-5}{9}$.
A. $\dfrac{-1}{3}$.
B. $\dfrac{-5}{3}$.
C. $\dfrac{-1}{9}$.
D. $\dfrac{-5}{9}$.
Ta có $\int\limits_{0}^{1}{\left( {{x}^{2}}-2x-3f\left( x \right) \right)\text{d}x=1}\Leftrightarrow \left. \left( \dfrac{{{x}^{3}}}{3}-{{x}^{2}} \right) \right|_{0}^{1}-3\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=1\Leftrightarrow \dfrac{-2}{3}-3\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=1$
$\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\dfrac{-5}{9}$.
$\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}=\dfrac{-5}{9}$.
Đáp án D.