What is the integral from-2 to 3 of |x^2-1| ?

The integral from-2 to 3 of |x^2-1| is 28/3

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integral from-2 to 3 of |x^2-1|

\int_{- 2}^{3} x^{2} - 1 d x

\frac{28}{3}

Decimal

9.33333 \dots

Solution steps

\int_{- 2}^{3} x^{2} - 1 d x

Eliminate Absolutes

= \int_{- 2}^{- 1} x^{2} - 1 d x + \int_{- 1}^{1} - x^{2} + 1 d x + \int_{1}^{3} x^{2} - 1 d x

\int_{- 2}^{- 1} x^{2} - 1 d x = \frac{4}{3}

\int_{- 1}^{1} - x^{2} + 1 d x = \frac{4}{3}

\int_{1}^{3} x^{2} - 1 d x = \frac{20}{3}

= \frac{4}{3} + \frac{4}{3} + \frac{20}{3}

Simplify

\frac{4}{3} + \frac{4}{3} + \frac{20}{3} : \frac{28}{3}

= \frac{28}{3}

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What is the integral from-2 to 3 of |x^2-1| ?
The integral from-2 to 3 of |x^2-1| is 28/3