Cho \(\int\limits_0^1 {\left[ {f\left( x \right) – 2g\left( x \right)} \right]{\rm{d}}x} = 12\) & \(\int\limits_0^1 {g\left( x \right){\rm{d}}x} =

* Hướng dẫn giải

Ta có:

\(\int\limits_0^1 {\left[ {f\left( x \right) – 2g\left( x \right)} \right]{\rm{d}}x} = \int\limits_0^1 {f\left( x \right){\rm{d}}x} – 2\int\limits_0^1 {g\left( x \right){\rm{d}}x} \)

\( \Rightarrow \int\limits_0^1 {f\left( x \right){\rm{d}}x} = \int\limits_0^1 {\left[ {f\left( x \right) – 2g\left( x \right)} \right]{\rm{d}}x} + 2\int\limits_0^1 {g\left( x \right){\rm{d}}x} = 12 + 2.5 = 22\)