Evaluate ∫-11|x4-x|dx. - Mathematics

Question

Evaluate $\int_{- 1}^{1} | x^{4} - x | d x$ .

Sum

Solution

Let I = $\int_{- 1}^{1} | x^{4} - x | d x$

= $\int_{- 1}^{0} (x^{4} - x) d x - \int_{0}^{1} (x^{4} - x) d x$

= ${[\frac{x^{5}}{5} - \frac{x^{2}}{2}]}_{- 1}^{0} - {[\frac{x^{5}}{5} - \frac{x^{2}}{2}]}_{0}^{1}$

= $[(0 - 0) - (\frac{- 1}{5} - \frac{1}{2})] - [(\frac{1}{5} - \frac{1}{2}) - 0]$

= $\frac{7}{10} + \frac{3}{10}$

= 1.

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Evaluate ∫-11|x4-x|dx. - Mathematics

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