What is the integral from-3 to 0 of (6x^3-3x^2-9x-6) ?

The integral from-3 to 0 of (6x^3-3x^2-9x-6) is -126

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integral from-3 to 0 of (6x^3-3x^2-9x-6)

\int_{- 3}^{0} (6 x^{3} - 3 x^{2} - 9 x - 6) d x

- 126

Solution steps

\int_{- 3}^{0} 6 x^{3} - 3 x^{2} - 9 x - 6 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_{- 3}^{0} 6 x^{3} d x - \int_{- 3}^{0} 3 x^{2} d x - \int_{- 3}^{0} 9 x d x - \int_{- 3}^{0} 6 d x

\int_{- 3}^{0} 6 x^{3} d x = - \frac{243}{2}

\int_{- 3}^{0} 3 x^{2} d x = 27

\int_{- 3}^{0} 9 x d x = - \frac{81}{2}

\int_{- 3}^{0} 6 d x = 18

= - \frac{243}{2} - 27 - (- \frac{81}{2}) - 18

Simplify

- \frac{243}{2} - 27 - (- \frac{81}{2}) - 18 : - 126

= - 126

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What is the integral from-3 to 0 of (6x^3-3x^2-9x-6) ?
The integral from-3 to 0 of (6x^3-3x^2-9x-6) is -126