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

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

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

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

- \frac{9}{4}

Decimal

- 2.25

Solution steps

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

Expand

x (x - 2) (x + 1) : 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}

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

\int_{- 1}^{2} e^{x + 1} d x

\int_{0}^{1} \frac{x}{1 + 6 x ^{2}} d x

\int_{0}^{4} (x^{2} + x) d x

\int_{1}^{3} (\frac{3}{4} x^{2} - 2) d x

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