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

The integral from 0 to 2 of (x^3-3x+3) is 4

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

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

4

Solution steps

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

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} 3 x d x = 6

\int_{0}^{2} 3 d x = 6

= 4 - 6 + 6

Simplify

= 4

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\int_{2}^{0} x d x

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