What is the integral from-0.5 to 3.5 of x^3-6x^2+8x ?

The integral from-0.5 to 3.5 of x^3-6x^2+8x is -0.5

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integral from-0.5 to 3.5 of x^3-6x^2+8x

\int_{- 0.5}^{3.5} x^{3} - 6 x^{2} + 8 x d x

- 0.5

Solution steps

\int_{- 0.5}^{3.5} x^{3} - 6 x^{2} + 8 x 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_{- 0.5}^{3.5} x^{3} d x - \int_{- 0.5}^{3.5} 6 x^{2} d x + \int_{- 0.5}^{3.5} 8 x d x

\int_{- 0.5}^{3.5} x^{3} d x = 37.5

\int_{- 0.5}^{3.5} 6 x^{2} d x = 86

\int_{- 0.5}^{3.5} 8 x d x = 48

= 37.5 - 86 + 48

Simplify

= - 0.5

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What is the integral from-0.5 to 3.5 of x^3-6x^2+8x ?
The integral from-0.5 to 3.5 of x^3-6x^2+8x is -0.5