What is the integral from-1 to 0 of 2x^3-3x^2-12x ?

The integral from-1 to 0 of 2x^3-3x^2-12x is 9/2

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integral from-1 to 0 of 2x^3-3x^2-12x

\int_{- 1}^{0} 2 x^{3} - 3 x^{2} - 12 x d x

\frac{9}{2}

Decimal

4.5

Solution steps

\int_{- 1}^{0} 2 x^{3} - 3 x^{2} - 12 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_{- 1}^{0} 2 x^{3} d x - \int_{- 1}^{0} 3 x^{2} d x - \int_{- 1}^{0} 12 x d x

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

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

\int_{- 1}^{0} 12 x d x = - 6

= - \frac{1}{2} - 1 - (- 6)

Simplify

- \frac{1}{2} - 1 - (- 6) : \frac{9}{2}

= \frac{9}{2}

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What is the integral from-1 to 0 of 2x^3-3x^2-12x ?
The integral from-1 to 0 of 2x^3-3x^2-12x is 9/2