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Câu hỏi: Cho tích phân $\int\limits_{1}^{2}{\left[ 4f\left( x \right)-2x \right]\text{d}x}=1.$ Khi đó $\int\limits_{1}^{2}{f\left( x \right)}\text{d}x$ bằng
A. $-3$.
B. $-1$.
C. $1$.
D. $3$.
A. $-3$.
B. $-1$.
C. $1$.
D. $3$.
Ta có $\int\limits_{1}^{2}{\left[ 4f\left( x \right)-2x \right]\text{d}x}=1\Leftrightarrow 4\int\limits_{1}^{2}{f\left( x \right)\text{d}x-2\int\limits_{1}^{2}{x\text{d}x}}=1$
$\Leftrightarrow 4\int\limits_{1}^{2}{f\left( x \right)dx-2.}\dfrac{{{x}^{2}}}{2}\left| _{\begin{smallmatrix}
\\
1
\end{smallmatrix}}^{\begin{smallmatrix}
2 \\
\end{smallmatrix}} \right.=1\Leftrightarrow 4\int\limits_{1}^{2}{f\left( x \right)\text{d}x=4\Leftrightarrow }\int\limits_{1}^{2}{f\left( x \right)\text{d}x=1}.$
$\Leftrightarrow 4\int\limits_{1}^{2}{f\left( x \right)dx-2.}\dfrac{{{x}^{2}}}{2}\left| _{\begin{smallmatrix}
\\
1
\end{smallmatrix}}^{\begin{smallmatrix}
2 \\
\end{smallmatrix}} \right.=1\Leftrightarrow 4\int\limits_{1}^{2}{f\left( x \right)\text{d}x=4\Leftrightarrow }\int\limits_{1}^{2}{f\left( x \right)\text{d}x=1}.$
Đáp án C.