What is the integral from-4 to 4 of |x^2+x-2| ?

The integral from-4 to 4 of |x^2+x-2| is 107/3

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integral from-4 to 4 of |x^2+x-2|

\int_{- 4}^{4} x^{2} + x - 2 d x

\frac{107}{3}

Decimal

35.66666 \dots

Solution steps

\int_{- 4}^{4} x^{2} + x - 2 d x

Eliminate Absolutes

= \int_{- 4}^{- 2} x^{2} + x - 2 d x + \int_{- 2}^{1} - x^{2} - x + 2 d x + \int_{1}^{4} x^{2} + x - 2 d x

\int_{- 4}^{- 2} x^{2} + x - 2 d x = \frac{26}{3}

\int_{- 2}^{1} - x^{2} - x + 2 d x = \frac{9}{2}

\int_{1}^{4} x^{2} + x - 2 d x = \frac{45}{2}

= \frac{26}{3} + \frac{9}{2} + \frac{45}{2}

Simplify

\frac{26}{3} + \frac{9}{2} + \frac{45}{2} : \frac{107}{3}

= \frac{107}{3}

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What is the integral from-4 to 4 of |x^2+x-2| ?
The integral from-4 to 4 of |x^2+x-2| is 107/3