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

The integral from 0 to 2 of (-2x^2-4) is -40/3

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integral from 0 to 2 of (-2x^2-4)

\int_{0}^{2} (- 2 x^{2} - 4) d x

- \frac{40}{3}

Decimal

- 13.33333 \dots

Solution steps

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

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} 4 d x = 8

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

Simplify

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

= - \frac{40}{3}

What is the integral from 0 to 2 of (-2x^2-4) ?
The integral from 0 to 2 of (-2x^2-4) is -40/3