Khi đó Lim f( x ){d}}x} bằng:

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Biết \[\int\limits_0^1 {\left[ {f\left( x \right) + 2x} \right]} \,dx = 3\]. Khi đó \[\int\limits_0^1 {f\left( x \right){\rm{d}}x} \] bằng:

\(1\).

\(5\).

\(3\).

\(2\).

Giải thích

Ta có \[\int\limits_0^1 {\left[ {f\left( x \right) + 2x} \right]} \,dx = 3 \Leftrightarrow \int\limits_0^1 {f\left( x \right)\,} dx + 2\int\limits_0^1 x dx = 3 \Leftrightarrow \int\limits_0^1 {f\left( x \right)} \,dx + \left. {2 \cdot \frac{{{x^2}}}{2}} \right|_0^1 = 3\].

Suy ra \(\int\limits_0^1 {f\left( x \right){\rm{d}}x} = 3 - \left. {{x^2}} \right|_0^1 = 3 - \left( {1 - 0} \right) = 2\). Chọn D.