Nếu \(\int\limits_0^1 {2f\left( x \right){\rm{d}}x = 6} \) thì \(\int\limits_0^1 {\left[ {\dfrac{1}{3}f\left( x
Nếu \(\int\limits_0^1 {2f\left( x \right){\rm{d}}x = 6} \) thì \(\int\limits_0^1 {\left[ {\dfrac{1}{3}f\left( x \right) + 2x} \right]{\rm{d}}x} \) bằng
Đáp án đúng là: D
Ta có \(\int\limits_0^1 {\left[ {\dfrac{1}{3}f\left( x \right) + 2x} \right]{\rm{d}}x} = \dfrac{1}{3}\int\limits_0^1 {f\left( x \right){\rm{d}}x} + 2\int\limits_0^1 {x{\rm{d}}x} = \dfrac{1}{6}\int\limits_0^1 {2f\left( x \right){\rm{d}}x} + \left. {{x^2}} \right|_0^1 = \dfrac{1}{6}.6 + 1 = 2\).
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