Cho \(\int\limits_0^1 {f\left( x \right){\rm{d}}x}  = 2\) và \(\int\limits_0^1 {g\left( x \right){\rm{d}}x}  = 5\) khi đó \(\in

* Hướng dẫn giải

Ta có \(\int\limits_0^1 {g\left( x \right){\rm{d}}x}  = 5 \Leftrightarrow 2\int\limits_0^1 {g\left( x \right){\rm{d}}x}  = 10 \Leftrightarrow \int\limits_0^1 {2g\left( x \right){\rm{d}}x}  = 10\)

Xét \(\int\limits_0^1 {\left[ {f\left( x \right) - 2g\left( x \right)} \right]{\rm{d}}x}  = \int\limits_0^1 {f\left( x \right){\rm{d}}x}  - \int\limits_0^1 {2g\left( x \right){\rm{d}}x}  = 2 - 10 =  - 8\) .