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

The integral from-2 to 1 of 2x-x^2-x^3 is -9/4

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

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

- \frac{9}{4}

Decimal Notation

- 2.25

Solution steps

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

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

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

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

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

Simplify

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

= - \frac{9}{4}

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What is the integral from-2 to 1 of 2x-x^2-x^3 ?
The integral from-2 to 1 of 2x-x^2-x^3 is -9/4