Cho \(\int\limits_2^5 {f\left( x \right){\rm{d}}x} = 10\) khi đó \(\int\limits_5^2 {\left[ {2 - 4f\left( x \right)} \right]{\rm{d}}x} \) bằng

Lời giải

Ta có \(\int\limits_5^2 {\left[ {2 - 4f\left( x \right)} \right]{\rm{d}}x} = \int\limits_5^2 {{\rm{2d}}x} - \int\limits_5^2 {4f\left( x \right){\rm{d}}x} \)

\( = \int\limits_5^2 {{\rm{2d}}x} - 4\int\limits_5^2 {f\left( x \right){\rm{d}}x} \)

\( = - 6 + 4\int\limits_2^5 {f\left( x \right){\rm{d}}x} \)

\( = - 6 + 40 = 34\).

Chọn đáp án C