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

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

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

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

4

Solution steps

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

\int_{- 1}^{1} \frac{1}{2} x^{3} d x = 0

\int_{- 1}^{1} 2 x d x = 0

\int_{- 1}^{1} 2 d x = 4

= 0 - 0 + 4

Simplify

= 4

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