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Câu hỏi: Biết $\int\limits_{0}^{1}{\left[ f\left( x \right)+2x \right]}dx=3$. Khi đó $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$ bằng
A. $1$.
B. $5$.
C. $3$.
D. $2$.
A. $1$.
B. $5$.
C. $3$.
D. $2$.
Ta có $\int\limits_{0}^{1}{\left[ f\left( x \right)+2x \right]}dx=3\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)}dx+2\int\limits_{0}^{1}{x}dx=3\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)}dx+2.\dfrac{{{x}^{2}}}{2}\left| \begin{matrix}
1 \\
0 \\
\end{matrix} \right.=3$.
Suy ra $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=3-{{x}^{2}}\left| \begin{matrix}
1 \\
0 \\
\end{matrix} \right.=3-\left( 1-0 \right)=2$.
1 \\
0 \\
\end{matrix} \right.=3$.
Suy ra $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}=3-{{x}^{2}}\left| \begin{matrix}
1 \\
0 \\
\end{matrix} \right.=3-\left( 1-0 \right)=2$.
Đáp án D.