Nếu 4 ∫ 1 k f ( x ) d x = 5 thì k ∈ ( 1 ; 2 ) .

d) Sai. \(\int\limits_1^4 {kf\left( x \right){\rm{d}}x = k} \int\limits_1^4 {f\left( x \right){\rm{d}}x}  = k\left[ {F\left( 4 \right) - F\left( 1 \right)} \right] = k\left( {9 + 4\ln 2 - \frac{3}{2}} \right) = k\left( {\frac{{15}}{2} + 4\ln 2} \right)\).

Suy ra \(\int\limits_1^4 {kf\left( x \right){\rm{d}}x = 5}  \Leftrightarrow k\left( {\frac{{15}}{2} + 4\ln 2} \right) = 5 \Leftrightarrow k = \frac{5}{{\frac{{15}}{2} + 4\ln 2}} \approx 0,487 \notin \left( {1;2} \right)\).