What is the integral from-1 to 1 of x^3-2x^2-5x+6 ?

The integral from-1 to 1 of x^3-2x^2-5x+6 is 32/3

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integral from-1 to 1 of x^3-2x^2-5x+6

\int_{- 1}^{1} x^{3} - 2 x^{2} - 5 x + 6 d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{- 1}^{1} x^{3} - 2 x^{2} - 5 x + 6 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} 5 x d x + \int_{- 1}^{1} 6 d x

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

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

\int_{- 1}^{1} 5 x d x = 0

\int_{- 1}^{1} 6 d x = 12

= 0 - \frac{4}{3} - 0 + 12

Simplify

0 - \frac{4}{3} - 0 + 12 : \frac{32}{3}

= \frac{32}{3}

What is the integral from-1 to 1 of x^3-2x^2-5x+6 ?
The integral from-1 to 1 of x^3-2x^2-5x+6 is 32/3