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

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

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

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

- 4

Solution steps

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

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 3 x^{2} d x = 26

\int_{1}^{3} x d x = 4

\int_{1}^{3} 3 d x = 6

= 20 - 26 - 4 + 6

Simplify

= - 4

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