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

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

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integral from-2 to 1 of x((4-x^2)-(x+2))

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

- \frac{9}{4}

Decimal

- 2.25

Solution steps

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

Simplify

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

Expand

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

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

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

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

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

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

Simplify

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

= - \frac{9}{4}

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