What is the integral from-2 to 0 of (-x^2-2x) ?

The integral from-2 to 0 of (-x^2-2x) is 4/3

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integral from-2 to 0 of (-x^2-2x)

\int_{- 2}^{0} (- x^{2} - 2 x) d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

\int_{- 2}^{0} 2 x d x = - 4

= - \frac{8}{3} - (- 4)

Simplify

- \frac{8}{3} - (- 4) : \frac{4}{3}

= \frac{4}{3}

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What is the integral from-2 to 0 of (-x^2-2x) ?
The integral from-2 to 0 of (-x^2-2x) is 4/3