Nếu \(\int_0^2 {\left[ {3f\left( x \right) – x} \right]{\rm{d}}x} = 5\) thì \(\int_1^2 {f\left( x \right){\rm{d}}x} \) bằng

* Hướng dẫn giải

Ta có : \(\int_0^2 {\left[ {3f\left( x \right) – x} \right]{\rm{d}}x} = 3\int_0^2 {f\left( x \right){\rm{d}}x} – \int_0^2 {x{\rm{d}}x} = 3\int_0^2 {f\left( x \right){\rm{d}}x} – \left. {\frac{{{x^2}}}{2}} \right|_0^2 = 3\int_0^2 {f\left( x \right){\rm{d}}x} – 2\)

\( \Rightarrow \int_0^2 {f\left( x \right){\rm{d}}x} = \frac{{\int_0^2 {\left[ {3f\left( x \right) – x} \right]{\rm{d}}x} + 2}}{3} = \frac{7}{3}\)