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Câu hỏi: Nếu $\int\limits_{0}^{1}{\left[ 3f\left( x \right)+2g\left( x \right) \right]}\text{d}x=7$ và $\int\limits_{0}^{1}{g\left( x \right)}\text{d}x=-1$ thì $\int\limits_{0}^{1}{f\left( x \right)}\text{d}x$ bằng.
A. $3$.
B. $1$.
C. $-3$.
D. $-1$.
Ta có:
$\begin{aligned}
& \int\limits_{0}^{1}{\left[ 3f\left( x \right)+2g\left( x \right) \right]}\text{d}x=7 \\
& \Leftrightarrow 3\int\limits_{0}^{1}{f\left( x \right)}\text{d}x+2\int\limits_{0}^{1}{g\left( x \right)}\text{d}x=7 \\
& \Leftrightarrow 3\int\limits_{0}^{1}{f\left( x \right)}\text{d}x-2=7 \\
& \Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)}\text{d}x=3 \\
\end{aligned}$
A. $3$.
B. $1$.
C. $-3$.
D. $-1$.
Ta có:
$\begin{aligned}
& \int\limits_{0}^{1}{\left[ 3f\left( x \right)+2g\left( x \right) \right]}\text{d}x=7 \\
& \Leftrightarrow 3\int\limits_{0}^{1}{f\left( x \right)}\text{d}x+2\int\limits_{0}^{1}{g\left( x \right)}\text{d}x=7 \\
& \Leftrightarrow 3\int\limits_{0}^{1}{f\left( x \right)}\text{d}x-2=7 \\
& \Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)}\text{d}x=3 \\
\end{aligned}$
Đáp án A.