Cho \(\int\limits_0^1 {\left[ {f\left( x \right) - 2g\left( x \right)} \right]{\rm{d}}x} = 12\) và \(\int\limits_0^1 {g\left( x \right){\rm{d}}x} = 5\), khi đó \(\int\limits_0^1...

* Hướng dẫn giải

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

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