What is the integral from-5 to 5 of |x^2+x-6| ?

The integral from-5 to 5 of |x^2+x-6| is 65

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integral from-5 to 5 of |x^2+x-6|

\int_{- 5}^{5} x^{2} + x - 6 d x

65

Solution steps

\int_{- 5}^{5} x^{2} + x - 6 d x

Eliminate Absolutes

= \int_{- 5}^{- 3} x^{2} + x - 6 d x + \int_{- 3}^{2} - x^{2} - x + 6 d x + \int_{2}^{5} x^{2} + x - 6 d x

\int_{- 5}^{- 3} x^{2} + x - 6 d x = \frac{38}{3}

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

\int_{2}^{5} x^{2} + x - 6 d x = \frac{63}{2}

= \frac{38}{3} + \frac{125}{6} + \frac{63}{2}

Simplify

\frac{38}{3} + \frac{125}{6} + \frac{63}{2} : 65

= 65

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What is the integral from-5 to 5 of |x^2+x-6| ?
The integral from-5 to 5 of |x^2+x-6| is 65