Tính tích phân 8 ∫ 0 ∣ ∣ x 2 − 6 x ∣ ∣ d x .

Đáp án đúng là: A

\(\int\limits_0^8 {\left| {{x^2} - 6x} \right|dx} \)\( = \int\limits_0^6 {\left| {{x^2} - 6x} \right|dx} + \int\limits_6^8 {\left| {{x^2} - 6x} \right|dx} \)\( = \int\limits_0^6 {\left( { - {x^2} + 6x} \right)dx} + \int\limits_6^8 {\left( {{x^2} - 6x} \right)dx} \)

\( = \left. {\left( { - \frac{{{x^3}}}{3} + \frac{{6{x^2}}}{2}} \right)} \right|_0^6 + \left. {\left( {\frac{{{x^3}}}{3} - \frac{{6{x^2}}}{2}} \right)} \right|_6^8 = \frac{{152}}{3}\).