What is the integral from-2 to 0 of (x^3-3x^2-10x) ?

The integral from-2 to 0 of (x^3-3x^2-10x) is 8

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integral from-2 to 0 of (x^3-3x^2-10x)

\int_{- 2}^{0} (x^{3} - 3 x^{2} - 10 x) d x

8

Solution steps

\int_{- 2}^{0} x^{3} - 3 x^{2} - 10 x 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} x^{3} d x - \int_{- 2}^{0} 3 x^{2} d x - \int_{- 2}^{0} 10 x d x

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

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

\int_{- 2}^{0} 10 x d x = - 20

= - 4 - 8 - (- 20)

Simplify

= 8

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What is the integral from-2 to 0 of (x^3-3x^2-10x) ?
The integral from-2 to 0 of (x^3-3x^2-10x) is 8