Evaluate: ^ 1 _ -2 |x^ 3 - x | dx - Vidyadip

Question

Evaluate:
$\int\limits^{1}_{-2} \big|\text{x}^{3} - \text{x}\big| \text{ dx}$

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Answer

$\int\limits^{1}_{-2} \big|\text{x}^{3} - \text{x}\big| \text{ dx} = \int\limits^{-1}_{-2} - \text{(x}^{3} - \text{x})\text{dx} + \int\limits^{0}_{-1} \text{(x}^{3} - \text{x}) \text{dx} - \int\limits^{1}_{0} \text{(x}^{3} - \text{x}) \text{dx}$
$= \Bigg| \frac{\text{x}^{2}}{2} - \frac{\text{x}^{4}}{4}\Bigg|^{1}_{-2} + \Bigg|\frac{\text{x}^{4}}{4} - \frac{\text{x}^{2}}{2}\Bigg|^{0}_{-1} - \Bigg|\frac{\text{x}^{4}}{4} - \frac{\text{x}^{2}}{2}\Bigg|^{1}_{0}$
$= \frac{11}{4}$

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