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 Notation

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}

(x^{3} + 1) e^{x}

\int (x - 2)^{4} \frac{1}{4 x - x ^{2}} d x

\int (x^{2} + 7) e^{- x} d x

\frac{\partial}{\partial y} (3 x z^{3} e^{y^{2}})

x \to 2 lim (4 x^{2} + x + 4)

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