Cho hàm số f ( x ) = { 3x^2 − x + 1 k h i x ≥ 2 x − 1 khi x < 2 . Tích phân I = 3 ∫ 0 f ( x ) dx .

\(I = \int\limits_0^3 {f\left( x \right)dx} \)\( = \int\limits_0^2 {f\left( x \right)dx}  + \int\limits_2^3 {f\left( x \right)dx} \)\( = \int\limits_0^2 {\left( {x - 1} \right)dx}  + \int\limits_2^3 {\left( {3{x^2} - x + 1} \right)dx} \)

\( = \left. {\left( {\frac{{{x^2}}}{2} - x} \right)} \right|_0^2 + \left. {\left( {{x^3} - \frac{{{x^2}}}{2} + x} \right)} \right|_2^3\)\( = 2 + \frac{{35}}{2} = 19,5\).

Trả lời: 19,5.