What is the integral from 2 to 5 of (3x+x^2-x^3) ?

The integral from 2 to 5 of (3x+x^2-x^3) is -327/4

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integral from 2 to 5 of (3x+x^2-x^3)

\int_{2}^{5} (3 x + x^{2} - x^{3}) d x

- \frac{327}{4}

Decimal Notation

- 81.75

Solution steps

\int_{2}^{5} 3 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}^{5} 3 x d x + \int_{2}^{5} x^{2} d x - \int_{2}^{5} x^{3} d x

\int_{2}^{5} 3 x d x = \frac{63}{2}

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} x^{3} d x = \frac{609}{4}

= \frac{63}{2} + 39 - \frac{609}{4}

Simplify

\frac{63}{2} + 39 - \frac{609}{4} : - \frac{327}{4}

= - \frac{327}{4}

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What is the integral from 2 to 5 of (3x+x^2-x^3) ?
The integral from 2 to 5 of (3x+x^2-x^3) is -327/4