What is the integral from-5 to 3 of |x^2+x-12| ?

The integral from-5 to 3 of |x^2+x-12| is 61

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integral from-5 to 3 of |x^2+x-12|

\int_{- 5}^{3} x^{2} + x - 12 d x

61

Solution steps

\int_{- 5}^{3} x^{2} + x - 12 d x

Eliminate Absolutes

= \int_{- 5}^{- 4} x^{2} + x - 12 d x + \int_{- 4}^{3} - x^{2} - x + 12 d x

\int_{- 5}^{- 4} x^{2} + x - 12 d x = \frac{23}{6}

\int_{- 4}^{3} - x^{2} - x + 12 d x = \frac{343}{6}

= \frac{23}{6} + \frac{343}{6}

Simplify

\frac{23}{6} + \frac{343}{6} : 61

= 61

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What is the integral from-5 to 3 of |x^2+x-12| ?
The integral from-5 to 3 of |x^2+x-12| is 61