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

The integral from 0 to 3 of x^3-3x^2-x+3 is -9/4

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integral from 0 to 3 of x^3-3x^2-x+3

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

- \frac{9}{4}

Decimal

- 2.25

Solution steps

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

\int_{0}^{3} x^{3} d x = \frac{81}{4}

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} x d x = \frac{9}{2}

\int_{0}^{3} 3 d x = 9

= \frac{81}{4} - 27 - \frac{9}{2} + 9

Simplify

\frac{81}{4} - 27 - \frac{9}{2} + 9 : - \frac{9}{4}

= - \frac{9}{4}

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What is the integral from 0 to 3 of x^3-3x^2-x+3 ?
The integral from 0 to 3 of x^3-3x^2-x+3 is -9/4