What is the integral from-2 to 0 of (3x^3-x^2-9x-1) ?

The integral from-2 to 0 of (3x^3-x^2-9x-1) is 4/3

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integral from-2 to 0 of (3x^3-x^2-9x-1)

\int_{- 2}^{0} (3 x^{3} - x^{2} - 9 x - 1) d x

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

\int_{- 2}^{0} 3 x^{3} - x^{2} - 9 x - 1 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} 3 x^{3} d x - \int_{- 2}^{0} x^{2} d x - \int_{- 2}^{0} 9 x d x - \int_{- 2}^{0} 1 d x

\int_{- 2}^{0} 3 x^{3} d x = - 12

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

\int_{- 2}^{0} 9 x d x = - 18

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

= - 12 - \frac{8}{3} - (- 18) - 2

Simplify

- 12 - \frac{8}{3} - (- 18) - 2 : \frac{4}{3}

= \frac{4}{3}

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What is the integral from-2 to 0 of (3x^3-x^2-9x-1) ?
The integral from-2 to 0 of (3x^3-x^2-9x-1) is 4/3