What is the integral from-1 to 2 of x(x+1)(x-2) ?

The integral from-1 to 2 of x(x+1)(x-2) is -9/4

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integral from-1 to 2 of x(x+1)(x-2)

\int_{- 1}^{2} x (x + 1) (x - 2) d x

- \frac{9}{4}

Decimal

- 2.25

Solution steps

\int_{- 1}^{2} x (x + 1) (x - 2) d x

Expand

x (x + 1) (x - 2) : x^{3} - x^{2} - 2 x

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

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

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

= \frac{15}{4} - 3 - 3

Simplify

\frac{15}{4} - 3 - 3 : - \frac{9}{4}

= - \frac{9}{4}

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