What is the integral from-1 to 0 of (2x+x^2-x^3) ?

The integral from-1 to 0 of (2x+x^2-x^3) is -5/12

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integral from-1 to 0 of (2x+x^2-x^3)

\int_{- 1}^{0} (2 x + x^{2} - x^{3}) d x

- \frac{5}{12}

Decimal

- 0.41666 \dots

Solution steps

\int_{- 1}^{0} 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_{- 1}^{0} 2 x d x + \int_{- 1}^{0} x^{2} d x - \int_{- 1}^{0} x^{3} d x

\int_{- 1}^{0} 2 x d x = - 1

\int_{- 1}^{0} x^{2} d x = \frac{1}{3}

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

= - 1 + \frac{1}{3} - (- \frac{1}{4})

Simplify

- 1 + \frac{1}{3} - (- \frac{1}{4}) : - \frac{5}{12}

= - \frac{5}{12}

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What is the integral from-1 to 0 of (2x+x^2-x^3) ?
The integral from-1 to 0 of (2x+x^2-x^3) is -5/12