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

The integral from-2 to 2 of (x^3-3x+2) is 8

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

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

8

Solution steps

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

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

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

\int_{- 2}^{2} 2 d x = 8

= 0 - 0 + 8

Simplify

= 8

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What is the integral from-2 to 2 of (x^3-3x+2) ?
The integral from-2 to 2 of (x^3-3x+2) is 8