What is the integral from-4 to 4 of |x^2+x-6| ?

The integral from-4 to 4 of |x^2+x-6| is 109/3

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integral from-4 to 4 of |x^2+x-6|

\int_{- 4}^{4} x^{2} + x - 6 d x

\frac{109}{3}

Decimal Notation

36.33333 \dots

Solution steps

\int_{- 4}^{4} x^{2} + x - 6 d x

Eliminate Absolutes

= \int_{- 4}^{- 3} x^{2} + x - 6 d x + \int_{- 3}^{2} - x^{2} - x + 6 d x + \int_{2}^{4} x^{2} + x - 6 d x

\int_{- 4}^{- 3} x^{2} + x - 6 d x = \frac{17}{6}

\int_{- 3}^{2} - x^{2} - x + 6 d x = \frac{125}{6}

\int_{2}^{4} x^{2} + x - 6 d x = \frac{38}{3}

= \frac{17}{6} + \frac{125}{6} + \frac{38}{3}

Simplify

\frac{17}{6} + \frac{125}{6} + \frac{38}{3} : \frac{109}{3}

= \frac{109}{3}

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What is the integral from-4 to 4 of |x^2+x-6| ?
The integral from-4 to 4 of |x^2+x-6| is 109/3