What is the integral from-2 to 2 of |2-5x^2| ?

The integral from-2 to 2 of |2-5x^2| is 8sqrt(2/5)+56/3-(8sqrt(2))/(3sqrt(5))

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integral from-2 to 2 of |2-5x^2|

\int_{- 2}^{2} 2 - 5 x^{2} d x

8 \frac{2}{5} + \frac{56}{3} - \frac{8 2}{3 5}

Decimal

22.03976 \dots

Solution steps

\int_{- 2}^{2} 2 - 5 x^{2} d x

Eliminate Absolutes

= \int_{- 2}^{- \frac{2}{5}} - 2 + 5 x^{2} d x + \int_{- \frac{2}{5}}^{\frac{2}{5}} 2 - 5 x^{2} d x + \int_{\frac{2}{5}}^{2} - 2 + 5 x^{2} d x

\int_{- 2}^{- \frac{2}{5}} - 2 + 5 x^{2} d x = 2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5}

\int_{- \frac{2}{5}}^{\frac{2}{5}} 2 - 5 x^{2} d x = 4 \frac{2}{5} - \frac{4 2}{3 5}

\int_{\frac{2}{5}}^{2} - 2 + 5 x^{2} d x = 2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5}

= 2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5} + 4 \frac{2}{5} - \frac{4 2}{3 5} + 2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5}

Simplify

2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5} + 4 \frac{2}{5} - \frac{4 2}{3 5} + 2 \frac{2}{5} + \frac{28}{3} - \frac{2 2}{3 5} : 8 \frac{2}{5} + \frac{56}{3} - \frac{8 2}{3 5}

= 8 \frac{2}{5} + \frac{56}{3} - \frac{8 2}{3 5}

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What is the integral from-2 to 2 of |2-5x^2| ?
The integral from-2 to 2 of |2-5x^2| is 8sqrt(2/5)+56/3-(8sqrt(2))/(3sqrt(5))