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

The integral from-2 to 2 of |x|-x^2+2 is 20/3

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

\int_{- 2}^{2} ∣ x ∣ - x^{2} + 2 d x

\frac{20}{3}

Decimal

6.66666 \dots

Solution steps

\int_{- 2}^{2} ∣ x ∣ - x^{2} + 2 d x

Eliminate Absolutes

= \int_{- 2}^{0} - x - x^{2} + 2 d x + \int_{0}^{2} x - x^{2} + 2 d x

\int_{- 2}^{0} - x - x^{2} + 2 d x = \frac{10}{3}

\int_{0}^{2} x - x^{2} + 2 d x = \frac{10}{3}

= \frac{10}{3} + \frac{10}{3}

Simplify

\frac{10}{3} + \frac{10}{3} : \frac{20}{3}

= \frac{20}{3}

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What is the integral from-2 to 2 of |x|-x^2+2 ?
The integral from-2 to 2 of |x|-x^2+2 is 20/3