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

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

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integral from-1 to 1 of (|x|-x^2)

\int_{- 1}^{1} (∣ x ∣ - x^{2}) d x

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

\int_{- 1}^{1} ∣ x ∣ - x^{2} d x

Eliminate Absolutes

= \int_{- 1}^{0} - x - x^{2} d x + \int_{0}^{1} x - x^{2} d x

\int_{- 1}^{0} - x - x^{2} d x = \frac{1}{6}

\int_{0}^{1} x - x^{2} d x = \frac{1}{6}

= \frac{1}{6} + \frac{1}{6}

Simplify

\frac{1}{6} + \frac{1}{6} : \frac{1}{3}

= \frac{1}{3}

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