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

The integral from-1 to 1 of x^3-2x^2-x+2 is 8/3

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

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

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

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

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

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

= 0 - \frac{4}{3} - 0 + 4

Simplify

0 - \frac{4}{3} - 0 + 4 : \frac{8}{3}

= \frac{8}{3}

What is the integral from-1 to 1 of x^3-2x^2-x+2 ?
The integral from-1 to 1 of x^3-2x^2-x+2 is 8/3