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Câu hỏi: Cho $\int_{0}^{1}{\left( {{x}^{2}}-2x-3f\left( x \right) \right)\text{d}x}=1$. Tính $\int_{0}^{1}{f\left( x \right)\text{d}x}$.
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 $\int_{0}^{1}{\left( {{x}^{2}}-2x-3f\left( x \right) \right)dx}=1\Leftrightarrow \int_{0}^{1}{\left( {{x}^{2}}-2x \right)dx}-3\int_{0}^{1}{f\left( x \right)dx}=1\Leftrightarrow -\dfrac{2}{3}-3\int_{0}^{1}{f\left( x \right)dx}=1$
$\int_{0}^{1}{f\left( x \right)\text{d}x}=-\dfrac{5}{9}$
$\int_{0}^{1}{f\left( x \right)\text{d}x}=-\dfrac{5}{9}$
Đáp án D.