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

The integral from-2 to 2 of (-x^2-2) is -40/3

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

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

- \frac{40}{3}

Decimal

- 13.33333 \dots

Solution steps

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

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 2 d x = 8

= - \frac{16}{3} - 8

Simplify

- \frac{16}{3} - 8 : - \frac{40}{3}

= - \frac{40}{3}

What is the integral from-2 to 2 of (-x^2-2) ?
The integral from-2 to 2 of (-x^2-2) is -40/3