Cho ∫ f ( x ) d x = F ( x ) , ∫ g ( x ) d x = G ( x ) . Khi đó, I = ∫ [ 2 g ( x ) − f ( x ) ] d x bằng

2/20

Cho \[\int {f\left( x \right)dx = } F\left( x \right),{\rm{ }}\int {g\left( x \right)dx = G\left( x \right)} \]. Khi đó, \[I = \int {\left[ {2g\left( x \right) - f\left( x \right)} \right]dx} \] bằng

\[2F\left( x \right) + G\left( x \right).\]

\[2F\left( x \right) - G\left( x \right).\]

\[2G\left( x \right) - F\left( x \right).\]

\[F\left( x \right) - 2G\left( x \right).\]

Giải thích

Đáp án đúng là: C

Ta có: \[I = \int {\left[ {2g\left( x \right) - f\left( x \right)} \right]dx} \]

\[I = \int {2g\left( x \right)dx} - \int {f\left( x \right)dx} \]

\[I = 2\int {g\left( x \right)dx} - \int {f\left( x \right)dx} \]

\[I = 2G\left( x \right) - F\left( x \right)\]