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