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

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

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

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

\frac{9}{4}

Solution steps

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

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

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

\int_{- 1}^{2} 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-1 to 2 of x^2+2x-x^3 ?
The integral from-1 to 2 of x^2+2x-x^3 is 9/4