What is the integral from-2 to 0 of 8x+2x^2-x^3 ?

The integral from-2 to 0 of 8x+2x^2-x^3 is -20/3

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integral from-2 to 0 of 8x+2x^2-x^3

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

- \frac{20}{3}

Decimal

- 6.66666 \dots

Solution steps

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

\int_{- 2}^{0} 8 x d x = - 16

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

\int_{- 2}^{0} x^{3} d x = - 4

= - 16 + \frac{16}{3} - (- 4)

Simplify

- 16 + \frac{16}{3} - (- 4) : - \frac{20}{3}

= - \frac{20}{3}

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What is the integral from-2 to 0 of 8x+2x^2-x^3 ?
The integral from-2 to 0 of 8x+2x^2-x^3 is -20/3