What is the integral from-3 to 1 of x(x-1)(x+3) ?

The integral from-3 to 1 of x(x-1)(x+3) is 32/3

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integral from-3 to 1 of x(x-1)(x+3)

\int_{- 3}^{1} x (x - 1) (x + 3) d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{- 3}^{1} x (x - 1) (x + 3) d x

Expand

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

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

\int_{- 3}^{1} x^{3} d x = - 20

\int_{- 3}^{1} 2 x^{2} d x = \frac{56}{3}

\int_{- 3}^{1} 3 x d x = - 12

= - 20 + \frac{56}{3} - (- 12)

Simplify

- 20 + \frac{56}{3} - (- 12) : \frac{32}{3}

= \frac{32}{3}

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What is the integral from-3 to 1 of x(x-1)(x+3) ?
The integral from-3 to 1 of x(x-1)(x+3) is 32/3