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

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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