\(\int\limits_0^{1.5} [x^3]dx\)
\(= \int\limits_0^1 [x^3]dx + \int\limits_{1}^{2^\frac13} [x^3]dx + \int\limits_{3^\frac13}^{1.5}[x^3]dx\)
\(= \int \limits_0^1 0\,dx + \int\limits_1^{2^\frac13}1\,dx + \int\limits_{2^\frac13}^{3^\frac13} 2\,dx + \int\limits_{3^\frac 13}^{1.5} 3\,dx\)
\(= 2^\frac 13 - 1 + 2(3^\frac13 - 2^\frac13) + 3(1.5 - 3^\frac 13)\)
\(= - 2^\frac13 - 3^\frac 13 + 4.5- 1\)
\(= 3.5 - 2^\frac13 - 3^\frac13\)
\(\approx 0.7978\) (approx)
