What is the integral from 2 to 4 of (x^3-6x^2+8x) ?

The integral from 2 to 4 of (x^3-6x^2+8x) is -4

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integral from 2 to 4 of (x^3-6x^2+8x)

\int_{2}^{4} (x^{3} - 6 x^{2} + 8 x) d x

- 4

Solution steps

\int_{2}^{4} 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_{2}^{4} x^{3} d x - \int_{2}^{4} 6 x^{2} d x + \int_{2}^{4} 8 x d x

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 6 x^{2} d x = 112

\int_{2}^{4} 8 x d x = 48

= 60 - 112 + 48

Simplify

= - 4

What is the integral from 2 to 4 of (x^3-6x^2+8x) ?
The integral from 2 to 4 of (x^3-6x^2+8x) is -4