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Câu hỏi: Cho $\int_0^1 f(x) \mathrm{d} x=2$ và $\int_0^1[f(x)-2 g(x)] \mathrm{d} x=-8$. Tính tích phân $\int_0^1 g(x) \mathrm{d} x$.
A. -3 .
B. 5 .
C. -5 .
D. -6 .
A. -3 .
B. 5 .
C. -5 .
D. -6 .
$
\begin{aligned}
& \int_0^1[f(x)-2 g(x)] \mathrm{d} x=-8 \Leftrightarrow \int_0^1 f(x) \mathrm{d} x-\int_0^1 2 g(x) \mathrm{d} x=-8 \\
& \Leftrightarrow 2-2 \int_0^1 g(x) \mathrm{d} x=-8 \Leftrightarrow \int_0^1 g(x) \mathrm{d} x=5 .
\end{aligned}
$
\begin{aligned}
& \int_0^1[f(x)-2 g(x)] \mathrm{d} x=-8 \Leftrightarrow \int_0^1 f(x) \mathrm{d} x-\int_0^1 2 g(x) \mathrm{d} x=-8 \\
& \Leftrightarrow 2-2 \int_0^1 g(x) \mathrm{d} x=-8 \Leftrightarrow \int_0^1 g(x) \mathrm{d} x=5 .
\end{aligned}
$
Đáp án B.
